There are 2 different ways to unblock someone on Instagram. The first and easiest way is to go to their Profile on Instagram and click on “Unblock” button. But if you don’t remember their profile link URL or name, you can do it by going to Instagram app on your mobile phone > Your Profile > Settings > Privacy > Blocked Accounts. Here you have a list of users that you have blocked previously, you can Unblock any of them that you want by clicking on Unblock button in front of the user’s name.
Blocking and Unblocking someone will not send any notifications to them.