Party member in demonstration having to make haste (5,4)
I believe the answer is:
march hare
'party member' is the definition.
(from the tea party in Alice in Wonderland)
'demonstration having to make haste' is the wordplay.
'demonstration' becomes 'march' (type of protest or demonstration).
'having' is a charade indicator (letters next to each other).
'to make haste' becomes 'hare' (hare can mean to run fast).
'march'+'hare'='MARCH HARE'
'in' is the link.
(Other definitions for march hare that I've seen before include "Animal in state of wild behaviour, starting with 3rd month?" , "Character at the tea-party in Alice's Adventures in Wonderland" , "Supposedly mad creature" , "madness" , "character encountered by Alice" .)