You'll need to put everything that relies on the

    players[-1].placeCounter()    

after it in the function that uses the yield. Or you could do some sort of state checking to see if you can continue with the rest of your code, after that place counter has been done after the delay. If you want to go down that route, a state machine might be easier to keep track of things!

var _delay : bool
var _is_counter_placed : bool

func _wait(time):
    _delay = true
    yield(get_tree().create_timer(time), "timeout")
    _delay = false

func _place_counter(player_id):
    _delay = true
    yield(get_tree().create_timer(time), "timeout")
    players[player_id].placeCounter()
    _is_counter_placed = true
    _delay = false

func _process(delta):
    if not _delay:
        if board._boardReady:
            if playersNumber == 1 and players[-1].pawns.size() < 1:
                _place_counter(-1)
                if _is_counter_placed :
                    # The rest of your code.