Get rid of an outbuilding (4)
I believe the answer is:
shed
I believe this is a double definition.
'get rid' is the first definition.
(shed can mean to get rid of or discard)
'an outbuilding' is the second definition.
(outbuilding in a garden)
'of' is the link.
(Other definitions for shed that I've seen before include "Hut - throw off - Guardian cryptic crossword setter" , "that may be at bottom of garden?" , "Removed in garden hut" , "Get rid of - garden building" , "Drop - cast off" .)