暇 acts as an adjective here, which explains the な which is basically the 連体形 of the 活用語尾 (conjugative suffix).
暇 can also be a noun, but here it is not.
Your sentence means "since/because I have free time, become my partner" (lit. because it is free time, do partner).
Finally, I will answer your question assuming you meant to say: "what is the difference between (noun)+な and (adjective)+な?" (and not (verb)+な)
The basic difference between these two なs is that the な following an adjective is the 活用語尾 (conjugative suffix), whereas the な following a noun is the auxiliary 「だ」. Both conjugated in the 連体 form.
There is a very small difference between -na adjectives' conjugative suffix and the auxiliary 「だ」, which is only morphologic (meaning there is no difference in meaning): when we use an adjective in the 連体 form, what follows will always be な, for example:
On the other hand, a noun has no conjugation, it acts on its own, and the following な (if there is) is independant because it is an auxiliary verb, and not a conjugation attached to the noun.
「厄介な」ので = adjective (because he is troublesome)
「学生」「な」ので = noun (because he is a student)
Plus, we cannot always use 「な」 (だ) after a noun, but it is okay for an adjective to be followed by な in any case.