A drunk hanging around entrance to Cheltenham racecourse (5)
I believe the answer is:
ascot
'racecourse' is the definition.
(British racecourse)
'a drunk hanging around entrance to cheltenham' is the wordplay.
'drunk' becomes 'sot' (both can mean someone who drinks too much).
'hanging around' means one lot of letters goes inside another.
'entrance to' suggests taking the first letters.
The initial letter of 'cheltenham' is 'c'.
'sot' enclosing 'c' is 'scot'.
'a'+'scot'='ASCOT'
(Other definitions for ascot that I've seen before include "Where the Queen often sees racehorses" , "sporting venue" , "Society race meeting" , "Town with racecourse" , "English racecourse in Berkshire" .)