It is very possilbe to be an aggressive counter fighter, part of counter fighting is getting the opponent to react to you, then countering, this is considered leading a guy into your technique.
Counter fighters need their space. If a pressure fighter can get in and hammer on the body with hooks, knees, uppercuts, the counter fighter is finished. Maintaining space is number one. Use your front kicks and side kicks, and your jab. Guys who rush in usually are punching so their bodies are exposed, land a good push kick with the back leg, or a side kick with the front leg, and get him backing up.
If you sit there waiting for the guy to do something and then counter, and he's content to just sit there too, you have to move in on him and get out before he reacts, then move in on him with your counter. try using more feints, attacking from different angles.
If the guy wants to sit there, you're either
1) too advanced for him or he's afraid, in which case, you need to find a better or more aggressive sparring partner, or
2) not using enough feints and footwork to get the guy to react to you, causing him to open up, and providing you with the opportunity to nail him.
As for drills, practice moving in quickly to land your stuff and exiting out in a different direction. pracetice moving forward, and then diagonally out. practice moving back then suddenly moving forward and then diagonally out again. move forward stop, back up real quick and moving forward again when the guy opens up.
YouTube - Taekwondo Paddle Drill
YouTube - Taekwondo Drills Training
This is a good example, move in with something, back up, and move in again, this can be done with punches too
This one of Lyoto is good, the part where is dashing in and out between the cones when he is talking about plyometrics.
YouTube - Lyoto Machida Training For UFC 98 Video by BadBoy planetamma com br visit!
Here's a good example of a jab drill, the pad holder keeps walking in while the other person uses the jabs to stop aggressive movement, and when the holder gets too close, she circles and gets more space, clinching when they need to.
YouTube - JAB DRILL