Rise of member-supported clubs (5)
I believe the answer is:
climb
'rise' is the definition.
('climb' can be a synonym of 'rise')
'member-supported clubs' is the wordplay.
'member' becomes 'limb' (limb is a kind of member**).
'supported' says to put letters next to each other.
'clubs' becomes 'c' (abbreviation used in card games such as bridge).
'limb' after 'c' is 'CLIMB'.
'of' acts as a link.
(Other definitions for climb that I've seen before include "showing the way up" , "improve one's social status" , "Get a rise" , "Move upwards, ascend" , "increase" .)