Born to have endless desire (3)
I believe the answer is:
nee
'born' is the definition.
('nee' is 'born' in French)
'endless desire' is the wordplay.
'endless' means to remove the last letter.
'desire' becomes 'need' (needing is a kind of desiring).
'need' with its final letter taken away is 'NEE'.
'to have' acts as a link.
(Other definitions for nee that I've seen before include "(Of married woman) born (with name)" , "Used to show a married woman's single name" , "Born as (former name)" , "Born (female)" , "Adjective denoting woman's name before marriage" .)