He leaves the new rep without a function (7)
I believe the answer is:
tangent
'a function' is the definition.
(I know that tangent is a type of circular function)
'he leaves the new rep without' is the wordplay.
'leaves' suggests deleting specific letters.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'rep' becomes 'agent' (I've seen this in another clue).
'without' is an insertion indicator.
'the' with 'he' removed is 't'.
'n' going into 'agent' is 'angent'.
't'+'angent'='TANGENT'
(Other definitions for tangent that I've seen before include "Line touching circumference" , "Line grazing another" , "A new line of thought" , "mostly irrelevant item" , "Straight line that touches but does not intersect a circle" .)