Cut in housing a shame (4)
I believe the answer is:
gash
'cut' is the definition.
(I've seen this before)
'in housing a shame' is the wordplay.
'in' indicates a hidden word.
'GASH' is hidden within 'housing a shame'.
(Other definitions for gash that I've seen before include "Deep open cut" , "Deep, jagged tear" , "Cut deeply" , "Open wound" , "score heavily" .)