Performing solo with churlish outsiders in the academy (6)
I believe the answer is:
school
'academy' is the definition.
(I've seen this in another clue)
'performing solo with churlish outsiders' is the wordplay.
'performing' is an anagram indicator (the letters move around or 'perform').
'with' means one lot of letters goes inside another.
'outsiders' says to hollow out the word (remove centre letters) (only the letters on the outside of the word remain).
'churlish' with its middle taken out is 'ch'.
'solo' with letters rearranged gives 'sool'.
'sool' going around 'ch' is 'SCHOOL'.
'in the' acts as a link.
(Other definitions for school that I've seen before include "building" , "See 24" , "company that's all at sea" , "some bass?" , "See 7" .)