That lady's next in line, not I (3)
I believe the answer is:
her
'that lady's' is the definition.
(I've seen this before)
'next in line not i' is the wordplay.
'next in line' becomes 'heir' (I've seen this before).
'not' is a deletion indicator.
'heir' with 'i' taken away is 'HER'.
(Other definitions for her that I've seen before include "That lady's" , "That lady" , "The woman's" , "In the Midlands she" , "She, objectively" .)