Enter king, say, carrying head of Republican (6)
I believe the answer is:
pierce
'enter' is the definition.
(I've seen this before)
'king say carrying head of republican' is the wordplay.
'king say' becomes 'piece' (king is a kind of piece).
'carrying' indicates putting letters inside.
'head of' says to take the initial letters.
The initial letter of 'republican' is 'r'.
'piece' going around 'r' is 'PIERCE'.
(Other definitions for pierce that I've seen before include "Stick a pin in" , "Riddle" , "force way through" , "Enter" , "Bore hole through, perhaps ear" .)