Powerful Hookset is your 2nd "Hook" ability that uses GP. And it can only be used during Patience. Patience (+50% HQ chance that lasts 3 minutes) also gives you Inefficient Hooking (-40% chance of catching fish) so Powerful Hookset removes that effect. You use it like you'd normally "Hook."

You get Precision Hookset at lv. 56 which is your 3rd "Hook" ability. Also used during Patience. I am just not sure what the difference is between those two.

Oh, and you need to use Patience before you use "Cast."