She sang out “The key is inside” (5)
I believe the answer is:
agnes
'she' is the definition.
'sang out the key is inside' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'the key' becomes 'e' (I've seen this in other clues**).
'is inside' is an insertion indicator.
'sang' is an anagram of 'agns'.
'agns' placed around 'e' is 'AGNES'.
(Other definitions for agnes that I've seen before include "David's second wife" , "The Eve of St. - (Keats)" , "Patron saint of virgins" , "St --' Eve, poem by Lord Tennyson" , "Woman" .)