Open Instagram and go to your profile
Tap the post you want to hide
Tap the three dots in the top right corner
Select Archive
To hide multiple posts, archive each post one by one
To hide posts from a specific person, set your account to Private
To hide your posts from someone without blocking them, remove them as a follower if your account is private
To hide posts from your profile grid, archive them
To hide tagged posts, go to Settings and privacy
Tap Tags and mentions
Choose Manually approve tags
Remove yourself from unwanted tagged posts
To hide story posts, use Close Friends or hide your story from specific people in Story settings