Cleaner splitting big increase in extra payment (9)
I believe the answer is:
surcharge
'extra payment' is the definition.
(an extra or additional charge)
'cleaner splitting big increase' is the wordplay.
'cleaner' becomes 'char' (charwoman is a type of cleaner).
'splitting' is an insertion indicator.
'big increase' becomes 'surge'.
'char' going inside 'surge' is 'SURCHARGE'.
'in' is the link.
(Other definitions for surcharge that I've seen before include "Extra payment" , "Additional item on bill" , "Excess fee" , "extra amount" , "addition to cost" .)