The cleaner the better half will hire (7)
I believe the answer is:
charter
'will hire' is the definition.
'charter' can be an answer for 'hire' (I've seen this before). I'm not certain of the 'will' bit.
'the cleaner the better half' is the wordplay.
'the cleaner' becomes 'char' (charwoman is a type of cleaner).
'the better half' becomes 'ter'.
'char'+'ter'='CHARTER'
Can you help me to learn more?
(Other definitions for charter that I've seen before include "Hire - document granting privileges" , "Let or hire a ship or aircraft" , "Right or privilege" , "Contract to lease transportation" , "Hire (of aircraft/ship)" .)