Collins COBUILD Advanced Learner's English Dictionary - chase up

1. If you chase up something that is needed or needs dealing with, you find it or find out what is being done about it. When I didn’t hear from the suppliers or receive a refund, I chased the matter up... The authority can chase up the source of the pollution and demand that the owner clean it up. PHRASAL VERB: V n P, V P n (not pron) 2. If you chase someone up, you look for them and find them because you want them to do something or give you something. ...the story of a man who comes to Hollywood to chase up a client who has defaulted on a debt. = track down PHRASAL VERB: V P n (not pron), also V n P