American soldier on leave to look for escort (6)
I believe the answer is:
gigolo
'for escort' is the definition.
(term for a male escort)
'american soldier on leave to look' is the wordplay.
'american soldier' becomes 'GI' (informal term for a US soldier).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'leave' becomes 'go' (to go is to depart or leave).
'to look' becomes 'lo' (archaic exclamation meaning 'look!').
'gi'+'go'+'lo'='GIGOLO'
(Other definitions for gigolo that I've seen before include "Paid male lover" , "Old word for man maintained by rich woman" , "Woman's paid male escort" , "Hired male escort" , "Professional male escort" .)