Long periods of fame on Strictly (4)
I believe the answer is:
eons
'long periods' is the definition.
(I've seen this before)
'of fame on strictly' is the wordplay.
'of' says the answer is hidden in the clue.
'EONS' can be found hidden inside 'fame on strictly'.
(Other definitions for eons that I've seen before include "Endless periods" , "Very long periods (US)" , "Divisions of archaeological time" , "Long periods of time - noes have it" , "Times" .)