If you have moved clubs and no longer wish to follow along their results, you can simply unfollow that club through the PlayCricket App.
Open the app
Click on Competitions at the bottom of the screen
Click Add Club
Search the Club you wish to unfollow, by entering it in the search field
From the returned results, find the Club you are wishing to unfollow
Click the 'tick' sign next to the name of the Club, this will unfollow the club for you.
If you have done this correctly, you should see that 'tick' sign change back to a '+'. This means it is ready to be refollowed if you choose to in the future.