Beware, if you are thinking about to hack someone their Instagram account. If you want a direct answer on your question, if you can pay someone to hack a Instagram account for you, then the answer is “Yes”.
But, I should warn you, that it is highly illegal to perform this action, especially if it is not authorized by the Instagram account holder.
Can I pay someone to hack a Instagram account?
The fact is that you are trying to gain access to an account which does not belong to you, this is compared to burglary, as you will be able to “steal” all kind of information from the “Instagram account” you have breached, and in court, it will be VERY HARD for you to proof that you have not done anything with the information that you have seen from the breached Instagram account.
On underground markets, which are often only accessible via TOR and a trusted account, you will be able to find black hat hackers which provide these type of services. But ask yourself this, do you really want to ask a black hat hacker to hack a Instagram account for you? It is a very bad idea to do business with them. In the long run, you might be arrested for hiring someone to perform illegal actions for you.
ADVICE: Yes, it is possible, but NO, you should not do it.