She possibly dines with an egghead (6)
I believe the answer is:
denise
'she' is the definition.
(woman's name)
'possibly dines with an egghead' is the wordplay.
'possibly' indicates anagramming the letters.
'with' indicates putting letters inside.
'an egghead' becomes 'e' (head letter of 'egg').
'dines' anagrammed gives 'dnise'.
'dnise' placed around 'e' is 'DENISE'.
(Other definitions for denise that I've seen before include "Miss Van Outen" , "- - Lewis, pentathlete" .)