To unlock the Team Player trophy in Apex Legends, you must revive a teammate when they have been killed. Not when they are knocked down.
When a teammate is killed, head over to their loot box and press the Square button to recover their items. Amongst their loot, you will automatically pick up the dead teammates banner. You have 90 seconds to pick it up once they have been killed.
Once you have the dead teammates banner in your possession, you need to look for a Respawn Beacon. Unfortunately, the beacons are not marked on your map and the location is random for each match, so you will have to hunt around to find one.
Once you have found the Respawn Beacon, approach it and hold the Square button to begin reviving them. When the Respawn Team Members bar is full, your teammate will be dropped back into the match via a plane above.