How to make an AI Tank Turret follow the player? Whilst the tank is moving?

It may be best to do some experiments to see which way will work best for your setup, try both ways and check the performance impacts. Using a timer may work but you may end with a situation where the player moves a large distance in relation to the rotation of the turret between timer updates, in such a case the turret’s rotation would snap from one direction instantly to another in order to face the player again.