The term 'give CHASE' is an idiom that means to PURSUE or FOLLOW someone or something. This phrase can be broken down into several synonyms, each of which can be found in a crossword puzzle. The synonyms are HUNT (4 letters), CHASE (5 letters), HOUND (5 letters), TRAIL (5 letters), FOLLOW (6 letters), and PURSUE (6 letters). All of these words mean to actively seek out or track someone or something, usually with the intention of catching them.