I'm hopelessly gone on her! (6)
I believe the answer is:
imogen
'her' is the definition.
(I've seen this before)
'i'm hopelessly gone on' is the wordplay.
'i'm' becomes 'im' (**).
'hopelessly' is an anagram indicator.
'on' means one lot of letters goes inside another (as in clothing \'on\' a person).
'gone' anagrammed gives 'ogen'.
'im' placed into 'ogen' is 'IMOGEN'.
(Other definitions for imogen that I've seen before include "Shakespearean heroine" , "Princess in "Cymbeline"" , "girl" , "Character 8 [OF SHAKESPEARE]" , "Girl's name; go mine (anagram)" .)