Train monkey to do without man (5)
I believe the answer is:
drill
'train monkey' is the definition.
'drill' can be an answer for 'monkey' (drill is a kind of monkey). I am unsure of the 'train' bit.
'do without man' is the wordplay.
'do' becomes 'dill' (I can't explain this - if you can you should give a lot more credence to this answer).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'man' becomes 'r' (abbreviation for rook, a chess piece or 'man').
'dill' going around 'r' is 'DRILL'.
'to' acts as a link.
Can you help me to learn more?
(Other definitions for drill that I've seen before include "Training (to make holes?)" , "Bore; small furrow" , "it could get boring" , "Twilled cotton; soldiers' exercise" , "makes one exercise" .)