Interestingly the "clear within a turn" rule would mean that you could only rent a port from the player who's turn it is (unless you allow all players to use their ports at any time).

I also assume by paying you mean making an undesirable trade, unless you allow gifting through another house rule.

In some games I've seen the following: Player A (current turn) wants to trade wheat for a brick through Player B's port. Player A will trade 2 wheat and a bonus resource to Player B for x arbitrary resource. On Player B's turn they move the wheat through their harbour for a brick and trade this back to Player A for their x arbitrary resource back. Player B keeps the bonus resource as payment, and Player A gets usage of Player B's harbour. This couldn't happen in one turn as only the current player can use their harbour.