Wait for old judge to cough up (11)
I believe the answer is:
expectorate
'cough up' is the definition.
('expectorate' can be a synonym of 'cough up')
'wait for old judge' is the wordplay.
'wait for' becomes 'expect' ('expect' can be a synonym of 'wait for').
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'judge' becomes 'rate' (rating is a kind of judging).
'expect'+'o'+'rate'='EXPECTORATE'
'to' acts as a link.
(Other definitions for expectorate that I've seen before include "Cough up and spit out" , "clear throat" .)