Make break — not Bingham's first (5)
I believe the answer is:
reach
'make' is the definition.
(I know that make can be written as reach)
'break not bingham's first' is the wordplay.
'break' becomes 'breach' (synonyms).
'not' indicates named letters should be taken away.
'bingham's first' becomes 'b' (1st letter of 'bingham').
'breach' with 'b' removed is 'REACH'.
(Other definitions for reach that I've seen before include "Grasp" , "Arrive at the destination" , "compass" , "Put out the hand for a part of the river" , "Scope; get to" .)