Bill's partner fired up, calm down! (4,2)
I believe the answer is:
cool it
'calm down' is the definition.
(synonyms)
'bill's partner fired up' is the wordplay.
'bill's partner' becomes 'coo' (I've seen this in another clue).
'fired up' becomes 'lit' (I've seen this in another clue).
'coo'+'lit'='COOL IT'
(Other definitions for cool it that I've seen before include "In slang, calm down" , "Relax" , "Here's what to do before opening champagne" , "Modern expression for calm down, or reduce heat" , "Don't get so excited'" .)