Having a shot at something means to attempt or try something. Therefore, the antonyms for having a shot at would be to not attempt, to refrain from trying or to give up before even trying. Some words that convey these antonyms include surrender, abandon, quit, yield, relinquish, resign, and bow out. However, it is crucial to remember that giving up before trying is a negative characteristic, and it is always better to attempt something and fail than to not try at all. Success only comes when we make an effort and take a chance, even if it means having a shot at something we might not succeed in.