Wants niece's desk regularly scrubbed (5)
I believe the answer is:
needs
'wants' is the definition.
(needing is a kind of wanting)
'niece's desk regularly scrubbed' is the wordplay.
'regularly scrubbed' means one should take alternating letters (letters removed at regular intervals).
'nieces'+'desk'='niecesdesk'
The alternate letters of 'niecesdesk' are 'NEEDS'.
(Other definitions for needs that I've seen before include "What is required" , "shopping-list, say" , "Things that are wanted" , "Can't do without" , "Wants, requires" .)