Back in Birmingham’s first beat club (7)
I believe the answer is:
niblick
'club' is the definition.
(historical type of golf club)
'back in birmingham's first beat' is the wordplay.
'back' says the letters should be written backwards.
'first' suggests taking the first letters.
'beat' becomes 'lick' (synonyms).
The first letter of 'birmingham' is 'b'.
'in' backwards is 'ni'.
'ni'+'b'+'lick'='NIBLICK'
(Other definitions for niblick that I've seen before include "Golf iron" , "number eight say" , "old-fashioned club" , "Old golf club" , "No 9 iron" .)