Erudite composer shown the way out (7)
I believe the answer is:
learned
'erudite' is the definition.
(synonyms)
'composer shown the way out' is the wordplay.
'composer' becomes 'arne' (Thomas Arne, composer of 'Rule Britannia').
'shown the way' becomes 'led' (I've seen this in another clue).
'out' means one lot of letters goes inside another.
'arne' put inside 'led' is 'LEARNED'.
(Other definitions for learned that I've seen before include "Discovered - erudite" , "Well educated and knowledgeable" , "Discovered, ascertained" , "Studied" , "Came to know" .)