Erudite English composer in the outskirts of Leatherhead (7)
I believe the answer is:
learned
'erudite' is the definition.
('learned' can be a synonym of 'erudite')
'english composer in the outskirts of leatherhead' is the wordplay.
'english' becomes 'e' (abbreviation).
'composer' becomes 'arne' (I've seen this before**).
'in the' is an insertion indicator.
'outskirts of' means to remove the middle letters.
'leatherhead' with its centre removed is 'ld'.
'e'+'arne'='earne'
'earne' going into 'ld' is 'LEARNED'.
(Other definitions for learned that I've seen before include "Acquired information, being well educated" , "Gained understanding" , "Came to know" , "Highly educated" , "Discovered - erudite" .)