Work with old and extremely polite judge (7)
I believe the answer is:
operate
'work' is the definition.
('operate' can be a synonym of 'work')
'old and extremely polite judge' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'and' means one lot of letters go next to another.
'extremely' says to hollow out the word (remove centre letters).
'judge' becomes 'rate' (rating is a kind of judging).
'polite' with its middle removed is 'pe'.
'o'+'pe'+'rate'='OPERATE'
'with' is the link.
(Other definitions for operate that I've seen before include "Control, run, a mcahine say" , "Act in a theatre" , "Function; run" , "Work, run" , "Work as a surgeon" .)