Servile society that's rich (7)
I believe the answer is:
slavish
'servile' is the definition.
(similar in meaning)
'society that's rich' is the wordplay.
'society' becomes 's' (common abbreviation in names of organisations).
'that's rich' becomes 'lavish' (similar in meaning).
's'+'lavish'='SLAVISH'
(Other definitions for slavish that I've seen before include "Abjectly subservient" , "laborious" , "wasteful" , "Menial" , "Cringing" .)