From Longman Dictionary of Contemporary Englishcollect something ↔ up phrasal verb British Englishto pick up several things, and put them together SYN gather up Can you collect up all the dirty plates and cups? → collect→ See Verb table
Examples from the Corpus
collect up• And I also learned there is more to shell collecting than picking up a few for the condo coffee table.• Now she collects and builds up her stores all year round. 