Rubbish head of government consumed by bitterness (5)
I believe the answer is:
bilge
'rubbish' is the definition.
(thesaurus)
'head of government consumed by bitterness' is the wordplay.
'head of' indicates taking the first letters.
'consumed by' is an insertion indicator.
'bitterness' becomes 'bile' (I've seen this in other clues).
The initial letter of 'government' is 'g'.
'g' going within 'bile' is 'BILGE'.
(Other definitions for bilge that I've seen before include "Dirty water collecting on a vessel" , "Nonsense (informal)" , "Very long film, book etc" , "Rubbish - water in boat" , "Dirty water in bottom of boat - drivel - nonsense" .)