You can control your profile visibility to only show posts to approved followers, for this you can switch your profile to Private.
Switch your account to Private
To switch your account to Private:
- Tap on the profile
button or your Profile Photo in the bottom right to go to your profile. - Tap on the options
button to go to your settings. - Under Account section, locate Private Account option.
- Tap on the switch
next to it to toggle it on. Confirm when asked, the switch will turn blue to show that the Private Account option is turned on. People would have to send follow requests and only the ones you approve will be able to see your posts. It won't affect your existing followers. To switch back to public, simple toggle the switch back to off position.
Your visibility on Discover Page
If for some reason you want your photos to not be shown in Discover page, simply don't add any topics to your posts when creating a new posts. This also applies for related Topics and Hashtag screens.