She sang tipsily out of key (5)
I believe the answer is:
agnes
'she' is the definition.
'sang tipsily out of key' is the wordplay.
'tipsily' indicates anagramming the letters (in a drunk or tipsy way).
'out of' is an insertion indicator (some letters on the outside of others).
'key' becomes 'e' (musical key).
'sang' is an anagram of 'agns'.
'agns' going around 'e' is 'AGNES'.
(Other definitions for agnes that I've seen before include "Lady" , "Scandinavian singer" , "girl" , "Miss Grey" , "St --' Eve, poem by Lord Tennyson" .)