FITA (or now World Archery) Star awards are for Compound or Recurve archers who shoot the Gents FITA (Gents 1440) or Ladies FITA (Ladies 1440) round, shot in a tournament that has World Record Status.
Awards are for anyone shooting their appropriate FULL FITA round for their age & gender.
You can only claim the badges at the end of the tournament that you have just shot, the tournament organiser will have a form that you will need to complete.
You can only claim the badge relevant to your score. If you shoot your first round scoring 1101 – you can claim a Black badge – you cannot later on go back and claim your white badge.