Telekinetic DOFFs
From time to time, I see people in fleet chat looking for Telekinetic DOFFs. My answer used to be to send them one in the in game mail, but I've finally exhausted my supply of unbound telekinetics, so I figured instead, I'd just write up how to get one. There are a few DOFF missions that require a telekinetic DOFF, and these DOFFs don't drop from the normal methods.
There's really only one race that is guaranteed to have telekinesis, and that's the Vorta, which are fairly rare DOFFS. There's also 1 special, genetically modified DOFF that has telekinesis, Elizabeth Mohr (FED)/Mochaak (KDF).
With that out of the way, here's how to get some telekinetics:
Random DOFFs (these will be the unbound ones):
Method 1: Gamma Quadrant Duty Officer Mini-Pack and Gamma Quadrant Duty Officer Cadre:
These packs drop out of some of the older lockboxes and award 4 or 7 DOFFs from the Gamma Quadrant races respectively. Much like the Romulan Survivor Pack and Fleet Support Packs have small chances to drop liberated Borg and Bynar Doffs, these Gamma Quadrant packs can drop Vorta or Jem'Hadar ones. Vorta and Jem'Hadar will only be of Blue or better quality, so they will be incredibly rare out of the mini-pack, and pretty rare out of the cadre.
Method 2: Exchange Prisoners with the Dominion
This DOFF mission appears daily in the Alpha Quadrant under the Operations Officer tab. It requires and input of a Vorta or Jem'Hadar prisoner, which will always be of either blue or purple quality. This mission appears after completing the assignment chain Fugitives of Facility 4028 (http://sto.gamepedia.com/Assignment_chain:_Facility_4028_Fugitives). It is also of note that the Vorta prisoner has telekinesis as well, but most missions won't accept a prisoner as a valid input. The other repeatable mission of this chain is Strike Against Fugitive Support Network, when you get a critical success on this mission it will give you a new rare/very rare prisoner (which you can also reliably buy off the exchange). The Exchange Prisoners with the Dominion mission will remove the prisoner from your crew and grant you another DOFF, usually of blue or purple quality. Sometimes this will reward a Vorta or Jem'Hadar, but usually it is one of the other "Gamma Quadrant races" (For Fed that is Karemman, Caradassian, Bajoran, or Paradan, and for KDF it is Dosi, Ferasan, Cardassian, or Wadi).
So those 2 methods are for the risk takers, if you want guaranteed telekinetic DOFFS, here's how to go about it.
Method 1: Dominion Duty Officer (FED/KDF) (unbound)
This is a purple drop from the Dominion Lock Box. 1 of the doffs inside is a biologist named Seggis, she is telekinetic. This one is still semi-random in the sense that you may get a bunch of Jem'Hadar doffs before you get Seggis, but she is one of the pack rewards (you can also just buy her directly off the exchange, generally in the price range of 5 million ec).
Method 2: Elizabeth Mohr/Mochaak (bound)
Complete the DOFF mission chain Project Chrysalis (http://sto.gamepedia.com/Assignment_chain:_Project_Chrysalis), the final mission awards a purple adviser (note this is a civilian DOFF, so it doesn't always work as an input for some missions).
Method 3: Colonize the Zenas Expanse
This is a 7 part DOFF mission, so it'll probably take a little over a week to complete the chain. Like other colonization missions it will award a blue doff upon completion of Zenas Expanse Renown (7/7) and then unlock a repeatable mission, Support Zenas Expansion Colonization Efforts, which upon critical success will award a purple doff and a common refugee(fed) or prisoner (kdf). The reward for this one is a warp theorist that is a Vorta.
Method 4: Storyline Mission Facility 4028 (http://sto.gamepedia.com/Mission:_Facility_4028)
Completing this mission, which is part of the Dominion Domination storyline arc awards a Dominion Cadre which consists of 2 blue Jem'Hadar doffs (a Projectile Weapons Officer and an Energy Weapons Officer) and a purple Vorta Biochemist, Dathan. It is worth noting that if you put Dathan as one of your active ground duty officers, it will add Ketrecel White to your replicator menu which is nice if you're using the Jem'Hadar bridge officer that you get from this storyline arc as well.
So those are the big ways to get Telekinetic DOFFs, I'm sure there are some others, but those are what I've come across so far. If you've ever got DOFF questions (how to get certain DOFFs, how to access specific missions, buying/selling/trading strategies, etc...) feel free to hit me up either here or in game (handle is @crmonkey).
Happy DOFFing!
Edited to add (7/23/15): With the release of the Delta Alliance Duty Officer Pack in the c-store, there are new opportunities to get telekinetic doffs. Some of the Ocampan doffs that drop from the pack also have the telkinetic trait. While I wouldn't recommend cracking packs looking for a telekinetic, it does mean that they will be more available on the exchange. If you are looking for the specializations to look for (energy weapons officer, quartermaster, etc...) this is the link to the pack info: http://www.arcgames.com/en/games/star-trek-online/news/detail/9451433-star-trek-online%3A-delta-alliance-doffs
There's really only one race that is guaranteed to have telekinesis, and that's the Vorta, which are fairly rare DOFFS. There's also 1 special, genetically modified DOFF that has telekinesis, Elizabeth Mohr (FED)/Mochaak (KDF).
With that out of the way, here's how to get some telekinetics:
Random DOFFs (these will be the unbound ones):
Method 1: Gamma Quadrant Duty Officer Mini-Pack and Gamma Quadrant Duty Officer Cadre:
These packs drop out of some of the older lockboxes and award 4 or 7 DOFFs from the Gamma Quadrant races respectively. Much like the Romulan Survivor Pack and Fleet Support Packs have small chances to drop liberated Borg and Bynar Doffs, these Gamma Quadrant packs can drop Vorta or Jem'Hadar ones. Vorta and Jem'Hadar will only be of Blue or better quality, so they will be incredibly rare out of the mini-pack, and pretty rare out of the cadre.
Method 2: Exchange Prisoners with the Dominion
This DOFF mission appears daily in the Alpha Quadrant under the Operations Officer tab. It requires and input of a Vorta or Jem'Hadar prisoner, which will always be of either blue or purple quality. This mission appears after completing the assignment chain Fugitives of Facility 4028 (http://sto.gamepedia.com/Assignment_chain:_Facility_4028_Fugitives). It is also of note that the Vorta prisoner has telekinesis as well, but most missions won't accept a prisoner as a valid input. The other repeatable mission of this chain is Strike Against Fugitive Support Network, when you get a critical success on this mission it will give you a new rare/very rare prisoner (which you can also reliably buy off the exchange). The Exchange Prisoners with the Dominion mission will remove the prisoner from your crew and grant you another DOFF, usually of blue or purple quality. Sometimes this will reward a Vorta or Jem'Hadar, but usually it is one of the other "Gamma Quadrant races" (For Fed that is Karemman, Caradassian, Bajoran, or Paradan, and for KDF it is Dosi, Ferasan, Cardassian, or Wadi).
So those 2 methods are for the risk takers, if you want guaranteed telekinetic DOFFS, here's how to go about it.
Method 1: Dominion Duty Officer (FED/KDF) (unbound)
This is a purple drop from the Dominion Lock Box. 1 of the doffs inside is a biologist named Seggis, she is telekinetic. This one is still semi-random in the sense that you may get a bunch of Jem'Hadar doffs before you get Seggis, but she is one of the pack rewards (you can also just buy her directly off the exchange, generally in the price range of 5 million ec).
Method 2: Elizabeth Mohr/Mochaak (bound)
Complete the DOFF mission chain Project Chrysalis (http://sto.gamepedia.com/Assignment_chain:_Project_Chrysalis), the final mission awards a purple adviser (note this is a civilian DOFF, so it doesn't always work as an input for some missions).
Method 3: Colonize the Zenas Expanse
This is a 7 part DOFF mission, so it'll probably take a little over a week to complete the chain. Like other colonization missions it will award a blue doff upon completion of Zenas Expanse Renown (7/7) and then unlock a repeatable mission, Support Zenas Expansion Colonization Efforts, which upon critical success will award a purple doff and a common refugee(fed) or prisoner (kdf). The reward for this one is a warp theorist that is a Vorta.
Method 4: Storyline Mission Facility 4028 (http://sto.gamepedia.com/Mission:_Facility_4028)
Completing this mission, which is part of the Dominion Domination storyline arc awards a Dominion Cadre which consists of 2 blue Jem'Hadar doffs (a Projectile Weapons Officer and an Energy Weapons Officer) and a purple Vorta Biochemist, Dathan. It is worth noting that if you put Dathan as one of your active ground duty officers, it will add Ketrecel White to your replicator menu which is nice if you're using the Jem'Hadar bridge officer that you get from this storyline arc as well.
So those are the big ways to get Telekinetic DOFFs, I'm sure there are some others, but those are what I've come across so far. If you've ever got DOFF questions (how to get certain DOFFs, how to access specific missions, buying/selling/trading strategies, etc...) feel free to hit me up either here or in game (handle is @crmonkey).
Happy DOFFing!
Edited to add (7/23/15): With the release of the Delta Alliance Duty Officer Pack in the c-store, there are new opportunities to get telekinetic doffs. Some of the Ocampan doffs that drop from the pack also have the telkinetic trait. While I wouldn't recommend cracking packs looking for a telekinetic, it does mean that they will be more available on the exchange. If you are looking for the specializations to look for (energy weapons officer, quartermaster, etc...) this is the link to the pack info: http://www.arcgames.com/en/games/star-trek-online/news/detail/9451433-star-trek-online%3A-delta-alliance-doffs