One of my "go-to" singles drills is to start both players in the center of the baseline and rally several balls each back and forth to the middle of the court. Once the players are doing this successfully, I have them add trying to find a way to win the point.
One of my students gave me another great way to simulate the pressure during a longer pointing in an actual match. Each player tries to keep the ball in play until there have been five balls hit back and forth. Once the rally gets to five, each player attempts to get the opponent in trouble and then tries to win the point. The winner of the point receives the number of successful hits as their score for that point. The first person to reach or exceed 100 wins the game.
Using this scoring idea during the drill adds a lot of pressure to the situation and simulates what a player might feel when they are in a tight match and the points begin to get longer. Keep your focus on hitting one shot at a time and gradually increase your aggressiveness as the point gets longer.
The more you put yourself in this situation in practice, the more comfortable you will become in the longer points during an actual tennis match.