Recite so strangely in secret (8)
I believe the answer is:
esoteric
'secret' is the definition.
('esoteric' can be similar in meaning to 'secret')
'recite so strangely' is the wordplay.
'strangely' is an anagram indicator.
'recite'+'so'='reciteso'
'reciteso' anagrammed gives 'ESOTERIC'.
'in' is the link.
(Other definitions for esoteric that I've seen before include "exclusive" , "Secret, mysterious" , "I set core up to be mysterious" , "Inner - secret" , "Tie score (anagram)" .)