Cleaner wrongly supporting Greek cook (9)
I believe the answer is:
chargrill
'cook' is the definition.
(chargrilling is a type of cooking)
'cleaner wrongly supporting greek' is the wordplay.
'cleaner' becomes 'char' (charwoman is a type of cleaner).
'wrongly' becomes 'ill' (as in ill-advised, ill-gotten etc).
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'greek' becomes 'gr' (abbreviation for Greek).
'ill' after 'gr' is 'grill'.
'char'+'grill'='CHARGRILL'
(Other definitions for chargrill that I've seen before include "Cook quickly at a very high heat" , "put on barbecue" , "Cook with bare flames" .)