Would you like to see this as a core mechanic for one of the still unannounced civs?
Units would automatically gain prowess in combat, resulting in increased health and damage. This’d encourage the player to take better care of them, and the opponent to focus down or avoid veterans.
Experience would either be gained in a small area - i.e. a group of units would level up together - or veterans could give a small boost to experience gain when shuffled in with fresh recruits.
To offset this, units would cost more to recruit than with other civs but could become more powerful if taken care of. There are lots of other options of course, like giving them slow health regen when not in combat or a simple passive ability for balancing early vs late game.