Use 'finish up' to imply wrapping things up tidily towards the end of a task or project. Let's finish up this report, and then we can call it a day.
Pro Tip 2/3
Concluding Events
'Finish up' can indicate the final activities or actions in an event or gathering. We'll finish up the meeting with a quick Q&A session.
Pro Tip 3/3
Task Completion
Emphasizes the end point of an activity, especially when it has been lengthy or challenging. She was relieved to finish up her thesis after months of hard work.