She may possibly lie, even (6)
I believe the answer is:
eileen
'she' is the definition.
(I've seen this before)
'possibly lie even' is the wordplay.
'possibly' indicates anagramming the letters.
'even' becomes 'e'en' (old-fashioned contraction).
'lie' anagrammed gives 'eil'.
'eil'+'een'='EILEEN'
'may' is the link.
(Other definitions for eileen that I've seen before include "Girl's name" , "F. name; nee Eli (anag.)" , "Female name (including three letters E)" , "Female name (not beginning with A)" , "woman" .)