When looking for antonyms for the phrase "be after," it is important to understand the meaning of the phrase. "Be after" usually refers to pursuing or searching for something. Therefore, an antonym for this phrase would be to relinquish or abandon the search for something. Other antonyms could include giving up, surrendering, or forfeiting the pursuit of something. Additionally, the concept of not being interested in something could also be considered an antonym for "be after." Therefore, antonyms for "be after" would include phrases like "stop pursuing," "give up on," "not interested in," and "abandon the search for.