Serious composer imprisoned in Estonia (7)
I believe the answer is:
earnest
'serious' is the definition.
(similar in meaning)
'composer imprisoned in estonia' is the wordplay.
'composer' becomes 'arne' (Thomas Arne, composer of 'Rule Britannia').
'imprisoned in' indicates putting letters inside.
'estonia' becomes 'est' (abbreviation).
'arne' put inside 'est' is 'EARNEST'.
(Other definitions for earnest that I've seen before include "showing seriousness" , "Sneer at (anag) -- serious" , "Firm" , "Sincere in intention" , "Oscar Wilde play 'The Importance of Being . . . . . . .'" .)