finish up phrasal verb ( see also ↑ finish )
1 . British English informal to arrive at a particular place, after going to other places first SYN end up :
I took a long holiday in Italy and finished up in Rome.
2 . British English informal to get into a particular state or situation as the result of what you have done, especially without planning or expecting it SYN end up :
He tried to bribe a police officer and finished up in jail.
finish up with
Brett got into a fight and finished up with a broken wrist.
3 . finish something ↔ up to eat or drink all the rest of something, so there is none left:
Come on, finish up your drinks!