From Longman Dictionary of Contemporary Englishpick up after somebody phrasal verb informalto tidy things that someone else has left untidy I’m tired of picking up after you! → pick→ See Verb table
Examples from the Corpus
pick up after • The total numbers of teachers fell in the early 1980s and only began to pick up after 1983.• Ten people were picked up after four hours in the water, and the eleventh after five hours.• However, love will dictate that Tony at least pick up after himself.• Bonus: Promise to do any chore, even picking up after the dog.• When Lucy went around the dressing rooms picking up after the final number, her hands shook.• A penalty flag was thrown but picked up after the officials determined the contact was incidental.• But they can not seem to pick up after their dogs.• In our next issue we will be examining why some people still resist the pressure to pick up after their dogs.• I've been picking up after them all night and all morning. 