Right now in Worlds Adrift the grappling hook doesn’t level up or gain upgrades. This could always change, but right now it takes quite a bit of practice to get competent with it, and even longer to genuinely get good at it. So in some sense you do increase your skill by using it, but that leveling up happens in your brain and hands, not your computer!
The rope just like any other object within the game is also persistent in such a way that it can be wrapped about a tree.
Tips and tricks
Just like a pendulum if a player needed to speed up during the swing the rope must be shortened and for slowing down the rope would need to be lengthened.
If the player grapples on to a cannon shell right after another person fires it, it will launch the player very far forward depending on the power of the cannon, this can be used to reach islands quicker to find a suitable landing spot, or long distance ship boarding for combat.