Requires niece's dish to be scrubbed evenly (5)
I believe the answer is:
needs
'requires' is the definition.
('need' can be a synonym of 'require')
'niece's dish to be scrubbed evenly' is the wordplay.
'to be scrubbed evenly' indicates alternate letters (letters in even-numbered positions removed).
'nieces'+'dish'='niecesdish'
The alternating letters of 'niecesdish' are 'NEEDS'.
(Other definitions for needs that I've seen before include "Is desperate for" , "Wants, requires" , "necessity once" , "Requirements" , "Necessities" .)