First, you can either delete each search suggestion individually or clear all of them at once.
To delete individual suggestions, open the Instagram search bar and begin typing in whatever you’d like to search. The search suggestions should begin to populate. To delete one of them, just tap and hold on it and then select the “X” that appears in the upper left corner.
To clear all search suggestions, go to your Instagram profile page and select the “...” icon in the upper right corner. From the menu that appears, choose “Settings” and then scroll down to “Security.” Under “Security,” select “Clear Search History” and then confirm your selection. Instagram will then delete all of your search suggestions.
It’s also possible to adjust your search settings to prevent future suggestions. In the “Settings” menu, scroll down to “Privacy and Security,” then tap on “Search Contacts & Places.” From there, you can easily switch off the “Search & Account Suggestions” toggle. This will keep your searches private and prevent Instagram from showing you any search suggestions in the future.