Open the Google app on your iPhone
Tap your profile picture in the top right
Tap Search history
Tap Delete
Choose Delete today, Delete custom range, or Delete all time
Confirm the deletion
To delete individual searches
Open the Google app
Tap your profile picture
Tap Search history
Find the search you want to remove
Tap the X next to it
To delete Google search history in Safari
Open the Settings app
Tap Safari
Tap Clear History and Website Data
Confirm
To delete Google search history in Chrome
Open the Chrome app
Tap the three dots
Tap History
Tap Clear Browsing Data
Select Browsing History
Tap Clear Browsing Data
Confirm
To stop Google from saving future searches
Open the Google app
Tap your profile picture
Tap Search history
Tap Controls
Turn off Web & App Activity