Copied foreign character, delighted to be outside (8)
I believe the answer is:
emulated
'copied' is the definition.
('emulate' can be a synonym of 'copy')
'foreign character delighted to be outside' is the wordplay.
'foreign character' becomes 'mu' (Greek letter).
'delighted' becomes 'elated' (I've seen this before).
'to be outside' means one lot of letters goes inside another (some letters go outside others).
'mu' placed into 'elated' is 'EMULATED'.
(Other definitions for emulated that I've seen before include "Tried to equal or copy" , "Imitated" , "Male duet strove to equal" , "Rivalled" , "Tried hard to be as good as someone" .)