Being angry having lost leader, but getting on (5)
I believe the answer is:
aging
'getting on' is the definition.
(getting on means getting older)
'being angry having lost leader' is the wordplay.
'being angry' becomes 'raging' ('raging' can be a synonym of 'angry').
'having lost leader' means to remove the first letter.
'raging' with its initial letter taken off is 'AGING'.
'but' is the link.
(Other definitions for aging that I've seen before include "Getting old" , "Becoming more grown-up" , "Growing old in the US" , "Growing older" , "in decline" .)