Penny leaving Greek battle site for shack (4-2)
I believe the answer is:
lean-to
'shack' is the definition.
(thesaurus)
'penny leaving greek battle site' is the wordplay.
'penny' becomes 'p' (short for pence).
'leaving' is a deletion indicator.
'greek battle site' becomes 'Lepanto' (Battle of Lepanto, 1571).
'lepanto' with 'p' taken away is 'LEAN-TO'.
'for' is the link.
(Other definitions for lean-to that I've seen before include "Add-on building" , "It's roof slants against a wall" , "Shed built against wall" , "Building added to another" , "Simple building" .)