The Quick Claw doesn't prioritize any moves at all, rather makes them go first in situations they usually won't.
This means that Quick Claw will activate that one turn, but then for the rest of the five turns it will stay inactive. The user with Prankster (Liepard, in this case) will disable Quick Claw before it activates, however on that turn it has the chance of activating.
Here's a quote from smogon's page on Quick Claw:
>Similarly, a Pokemon with Prankster will move before a Pokemon using Custap Berry when using a non-attacking move.
As Custap berry and Quick Claw essentially do the same thing (though one hase to be consumed and is reliable) Prankster, or for that matter, any priority will go before Quick Claw.
Source: Experience and this.
Hope I helped!