How could the verb phrase 'tidy up' be put in Latin please?
The phrase 'tidy up' usually means 'return things to their proper places'. It may also, of course, include removing all the detritus of some operation.
In English we might say 'clear away' or 'sweep out', and 'tidy up'. If this is what you are looking for, then the verb verro, verri, versum is appropriate for both clearing and sweeping. The best option for making tidy, or 'putting things back (in their places)', is repono, reposui, repositum.
You could expand on the simple repono by adding in loca propria, 'in the proper places'. The context will decide if you need to do this.