Let off steam, in consequence rejecting leader (4)
I believe the answer is:
vent
'let off steam' is the definition.
(both can mean to release anger)
'consequence rejecting leader' is the wordplay.
'consequence' becomes 'event' (I've seen this in another clue).
'rejecting leader' means to remove the first letter.
'event' with its initial letter taken away is 'VENT'.
'in' acts as a link.
(Other definitions for vent that I've seen before include "Give outlet as to feelings" , "Outlet; slit in jacket" , "Discharge; give expression to" , "Small outlet" , "[BLOWHOLE] ?" .)