Chance of doing deal slim, initially (4)
I believe the answer is:
odds
'chance' is the definition.
(I've seen this in another clue)
'of doing deal slim initially' is the wordplay.
'initially' suggests taking the first letters.
The initial letters of 'of doing deal slim' is 'ODDS'.
(Other definitions for odds that I've seen before include "Partial darkness" , "inequality" , "Take chances" , "Betting likelihood" , "Likelihood of something happening" .)