Ages in Westgate-on-Sea (4)
I believe the answer is:
eons
'ages' is the definition.
(I know this)
'in westgate-on-sea' is the wordplay.
'in' indicates a hidden word.
'EONS' is hidden in the letters of 'westgate on sea'.
(Other definitions for eons that I've seen before include "Very long periods (US)" , "Divisions of geological time" , "Years and years" , "Long periods of time - noes have it" , "Vast ages" .)