Celebrated enthusiast not finishing by the sea (5)
I believe the answer is:
famed
'celebrated' is the definition.
(synonyms)
'enthusiast not finishing by the sea' is the wordplay.
'enthusiast' becomes 'fan' (fan is a kind of enthusiast).
'not finishing' means to remove the last letter.
'by' is a charade indicator (letters next to each other).
'the sea' becomes 'med' (abbreviation of Mediterranean).
'fan' with its final letter taken away is 'fa'.
'fa'+'med'='FAMED'
(Other definitions for famed that I've seen before include "Acclaimed" , "Eminent" , "Renowned" , "Noted" , "Well-known" .)