Greek character recording wild lions (7)
I believe the answer is:
epsilon
'greek character' is the definition.
(letter from the Greek alphabet)
'recording wild lions' is the wordplay.
'recording' becomes 'ep' (extended play vinyl record).
'wild' indicates an anagram.
'lions' with letters rearranged gives 'silon'.
'ep'+'silon'='EPSILON'
(Other definitions for epsilon that I've seen before include "character in Greece" , "small number mispronounced, almost completely the wrong way round" , "foreign letter" , "5th letter of the Greek alphabet" , "One's lip (anag)" .)