Behind the storehouse, down with this chap! (8)
I believe the answer is:
barnabas
'chap' is the definition.
(male given name)
'behind the storehouse down with' is the wordplay.
'behind' means one lot of letters go next to another.
'the storehouse' becomes 'barn' (storehouse for grain).
'down with' becomes 'a bas' (I've seen this before).
'barn'+'abas' is 'BARNABAS'.
'this' is the link.
(Other definitions for barnabas that I've seen before include "saint" , "missionary" , "one spreading the Word" .)