Synonyms for finish up

Most common

1. Clear up

get through informal, clear up, finish off, polish off

2. End up

end up, finish, land up, fetch up

Other

clew up informal UK

v. 1
To complete the last details of a task.
They were finishing up the dishes.
v. 2
To consume the last part of (something).
Do you want to finish up these cookies?

The small number after each word is its number of syllables (finish² = 2 syllables).