Sombre song for one gaining entry to cathedral city (5)
I believe the answer is:
elegy
'sombre song' is the definition.
(mournful song or poem)
'for one gaining entry to cathedral city' is the wordplay.
'for one' becomes 'eg' (both can mean 'for example').
'gaining entry to' is an insertion indicator.
'cathedral city' becomes 'ely' (English city with a cathedral).
'eg' inserted into 'ely' is 'ELEGY'.
(Other definitions for elegy that I've seen before include "Sorrowful poem/song" , "Poetic lament (in a country churchyard?)" , "A sorrowful poem - Gray wrote a famous one" , "Dirge" , "Mournful work" .)