From Longman Dictionary of Contemporary Englishchase somebody/something ↔ up phrasal verb British English1 REMIND/MAKE somebody REMEMBERto remind someone to do something they promised to do for you David hasn’t paid yet – you’d better chase him up.2 HURRYto try to make something happen or arrive more quickly, because it has been taking too long Can you chase up those photos for me tomorrow? → chase→ See Verb table
Examples from the Corpus
chase up• It should be easy to chase these people up.• It can be very annoying when you are wanting to hurry, chasing the cattle up a hill or something.• Recently I've made three dogs out of wood and cement, chasing a deer up a slope in Grizedale.• This gives you time to chase it up if there have been any hiccups.• Then he batted it to and fro, chasing it up one aisle and down another and slapping it silly.• A copper chased him up there.• When he saw Edwin Chase striding up towards them he made haste to make known one to the other.• Whatever pumped up your adrenaline, my darling, it took more than a chase to catch up with you. 