High class chief - he makes a withdrawal (3,6)
I believe the answer is:
top drawer
'high class' is the definition.
'top drawer' can be an answer for 'class' (I have seen 'highest class' mean 'top drawer' so perhaps 'class' could also mean 'top drawer'). I'm unsure of the 'high' bit.
'chief he makes a withdrawal' is the wordplay.
'chief' becomes 'top' (synonyms).
'he makes' becomes 'reward' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a withdrawal' is a reversal indicator.
'reward' written backwards gives 'drawer'.
'top'+'drawer'='TOP-DRAWER'
Can you help me to learn more?
(Other definitions for top drawer that I've seen before include "People of the highest standing" , "Highest social position - a furniture metaphor" , "high-class" , "Upper-class" , "upper class" .)