By arrangement, puts up about a third of the fee (5)
I believe the answer is:
setup
'by arrangement' is the definition.
'setup' can be an answer for 'arrangement' (thesaurus). I'm not certain of the 'by' bit.
'puts up about a third of the fee' is the wordplay.
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'about' indicates putting letters inside.
'a third of the fee' becomes 'e' (I can't justify this - if you can you should give a lot more credence to this answer).
'puts' backwards is 'stup'.
'stup' enclosing 'e' is 'SETUP'.
Can you help me to learn more?
(Other definitions for setup that I've seen before include "Organisation (informal)" , "Fix" .)