How to reactivate instagram account after permanently delete?

Hélas, I am afraid this is not possible. When you select permanent deletion, the process is irreversible.

Instagram provides a 30-day grace period. During this time, you can log in to stop the deletion. After those 30 days pass, your account is gone for good. All of your photos, followers, and messages are permanently erased from their servers. This is very different from deactivating, which is only a temporary measure.

Your only real option is to create a new account. You may be able to use your old username again, but only if another person has not already claimed it. It is a frustratingly strict policy, I know.