Lane close to Kent bores drunk musician (7)
I believe the answer is:
soloist
'musician' is the definition.
(soloist is a kind of musician)
'lane close to kent bores drunk' is the wordplay.
'lane close to kent' becomes 'lois' (Lois Lane, love interest of Clark Kent/Superman ).
'bores' means one lot of letters goes inside another (bore can mean to drill into).
'drunk' becomes 'sot' (synonyms).
'lois' inserted inside 'sot' is 'SOLOIST'.
(Other definitions for soloist that I've seen before include "Virtuoso player" , "this one's on his own" , "Individual musician" , "Lone performer" , "Single performer" .)