Decadent (6)
'decadent' is the definition.
(synonyms)
This is all the clue.
(Other definitions for effete that I've seen before include "Over-refined and ineffectual" , "Worn-out, decadent" , "Over-refined, pretentious" , "Enfeebled" , "Feeble, having lost vitatlity" .)
(Other definitions for rich that I've seen before include "Splendid" , "Containing a lot of fat, eggs and sugar" , "Having much money" , "Lord Chancellor" , "(Person) with plenty of money" .)