Perhaps put polish on or polish off (6)
I believe the answer is:
finish
I believe this is a double definition.
'perhaps put polish on' is the first definition.
(polish can mean to add a finish to something)
'polish off' is the second definition.
(to polish something off is to finish eating it)
'or' is the link.
(Other definitions for finish that I've seen before include "Bring to an end" , "Patina" , "train socially" , "'End, close (6)'" , "Conclusion or polish" .)