Famous divorce centre — wife coming to bad end (8)
I believe the answer is:
renowned
'famous' is the definition.
(I know that famous can be written as renowned)
'divorce centre wife coming to bad end' is the wordplay.
'divorce centre' becomes 'Reno' ('divorce capital of the world').
'wife' becomes 'w' (abbreviation).
'coming to' says to put letters next to each other.
'bad' is an anagram indicator.
'end' anagrammed gives 'ned'.
'reno'+'w'+'ned'='RENOWNED'
(Other definitions for renowned that I've seen before include "Famed" , "Distinguished" , "Widely known/respected" , "Famous, celebrated" , "Widely respected" .)