Behave stoically, but let the bile out (4,3,6)
I believe the answer is:
bite the bullet
'behave stoically' is the definition.
(to bite the bullet is to be stoic or brave)
'but let the bile out' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'but'+'let'+'the'+'bile'='butletthebile'
'butletthebile' anagrammed gives 'BITE THE BULLET'.
(Other definitions for bite the bullet that I've seen before include "Face up to trouble stoically" , "Face the music" , "resign oneself?" , "Be stoical" , "Decide on unpleasant action" .)