Among the objectives that you can be given, there are ones that ask you to either capture or kill an Elite target. Things can get a little muddled as the objectives appear very similar when they're handed out in-game.
Here's how to either capture or kill an Elite target in Rainbow Six Extraction.
Capturing an Elite Target
First up is the capture objective. This is probably the trickier and more dangerous of the two tasks. This is because the target must be kept alive and you have to lure it to the extraction point on the map.
The best way to do this is to clear as much of the map of enemies and nests before confronting the elite target. This way, you just need to get its attention and have it follow you to the extraction point. Once you arrive, interact with the raised keypad to set the trap and as soon as the target enters the extraction zone, they'll be captured.
Kill an Elite Target
Killing an Elite target comes in one of two varying objective types. You either have to stealth take down the target to get a sample of the parasite or lure them out and outright kill them in any way.
If it's a stealth objective, you'll be told to find the target straight away. If it's the more combat-focused objective, you'll be told to kill around 3 other enemies to lure out the Elite target.
You just need to focus on what the game is asking of you and things should be fairly simple from that point. With the stealth objective, as is the same with the capture objective, if you kill the Elite target (in this case, the wrong way) then the objective is failed. You can continue with the incursion but there is no way to reset the failed objective.
If you alert an Elite target, you can still take them down to get a parasite sample. Use a stun grenade on then and the take down option will be available for the duration of the stun.