Virtually hopeless wit (4)
I believe the answer is:
nous
'wit' is the definition.
(both can mean common sense)
'virtually hopeless' is the wordplay.
'virtually' means to remove the last letter (all but the last letter).
'hopeless' becomes 'no use' (if something is no use, it is hopeless or futile).
'nouse' with its final letter removed is 'NOUS'.
(Other definitions for nous that I've seen before include "Sound practical judgement" , "Informal common sense" , "We, in France, have common sense" , "Common sense (sl.)" , "Common-sense" .)