Privileged member wearing crimson is on the rise (7)
I believe the answer is:
insider
'privileged member' is the definition.
(I've seen this before)
'wearing crimson is on the rise' is the wordplay.
'wearing' becomes 'in' (wear in (and 'in' is fashionable)).
'crimson' becomes 'red' ('red' can be a synonym of 'crimson').
'on the rise' says the letters should be written in reverse.
'red'+'is'='redis'
'redis' written backwards gives 'sider'.
'in'+'sider'='INSIDER'
(Other definitions for insider that I've seen before include "One privy to knowledge as an organisation member" , "person in the club" , "member of favoured group?" , "Illegal sort of dealing" , "He's in the circle, knows the right people" .)