Before you try to acquire an inactive username, you have to make sure that the Instagram profile is actually inactive. Just because an account hasn’t posted in a while, doesn’t mean it’s an inactive account.
One of the options to know if the account is active or not is to follow that account. Then you can regularly check their activity through the “Following” tab to know if the account is actually inactive.
There’s no set procedure on Instagram to appeal for an inactive Instagram account, unless there’s a case of infringement or impersonation. If the inactive user account is an impersonation of your business/organization, you can
appeal here.
Please remember that you can acquire an inactive username on your trademark only if you have a registered trademark. If your trademark is not registered, there are minimal chances of acquiring the Instagram username.
Source:
https://www.quora.com/How-can-I-take-an-inactive-Instagram-username