Men in pursuit of earl and skinny woman (7)
I believe the answer is:
eleanor
'woman' is the definition.
'men in pursuit of earl and skinny' is the wordplay.
'men' becomes 'OR' (military abbreviation for Other Ranks).
'in pursuit of' means one lot of letters go next to another (some letters chase after others).
'earl' becomes 'e'.
'and' means one lot of letters go next to another.
'skinny' becomes 'lean' (similar in meaning).
'e'+'lean'='elean'
'or' after 'elean' is 'ELEANOR'.
(Other definitions for eleanor that I've seen before include "Real one (anag) - girl's name" , "Franklin D. Roosevelt's wife" , "Lady" , "woman" , "Wife of Henry II" .)