The point at which to find the middle-man? (6)
I believe the answer is:
centre
'the point' is the definition.
(centre is a kind of point)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for centre that I've seen before include "Place in the 18 down" , "See 7" , "Player" , "Middle, core" , "The point equidistant from everything" .)