Delivery supervisor behind mother bearing son (10)
I believe the answer is:
postmaster
'delivery supervisor' is the definition.
'behind mother bearing son' is the wordplay.
'behind' becomes 'post' (both can mean chronologically after**).
'mother' becomes 'mater' (old-fashioned term for mother).
'bearing' means one lot of letters goes inside another.
'son' becomes 's'.
'mater' enclosing 's' is 'master'.
'post'+'master'='POSTMASTER'
(Other definitions for postmaster that I've seen before include "who runs a local office?" , "Mail chief" .)