Rigid measure from head of state (5)
I believe the answer is:
ruler
This clue is a double definition.
'rigid measure' is the first definition.
(rigid tool for measuring things)
'head of state' is the second definition.
(ruler of a country)
'from' is the link.
(Other definitions for ruler that I've seen before include "Royal" , "One governing" , "One who commands - often seen in the classroom" , "Man in charge" , "Eg, king, emperor" .)