Cuts constraining Egypt's first pharaoh (6)
I believe the answer is:
cheops
'pharaoh' is the definition.
(I know that Cheops is a type of pharaoh)
'cuts constraining egypt's first' is the wordplay.
'cuts' becomes 'chops' (chopping is a kind of cutting).
'constraining' indicates putting letters inside.
'egypt's first' becomes 'e' (1st letter of 'egypt').
'chops' enclosing 'e' is 'CHEOPS'.
(Other definitions for cheops that I've seen before include "Pharaoh" , "Monumental builder" , "one buried in a huge monument" .)