Cooper? In short, one thing that coops (3,3)
I believe the answer is:
hen run
'thing that coops' is the definition.
(a hen run coops up hens)
'cooper? in short one' is the wordplay.
'cooper?' becomes 'Henry' (boxer Henry Cooper).
'in short' means to remove the last letter.
'one' becomes 'un' (northern English dialect form of 'one').
'henry' with its final letter removed is 'henr'.
'henr'+'un'='HEN-RUN'
(Other definitions for hen run that I've seen before include "Enclosure for fowls" , "Layers in such" .)