To finish up best (3)
I believe the answer is:
top
'best' is the definition.
('top' is associated in meaning with 'best')
'to finish up' is the wordplay.
'finish' indicates one should take the final letters.
The last letter of 'up' is 'p'.
'to'+'p'='TOP'
(Other definitions for top that I've seen before include "Children's toy" , "Upper side" , "Toy; uppermost point" , "The circus tent can be a big one" , "jumper, say?" .)