King Henry beginning to open Greek letter (3)
I believe the answer is:
rho
'greek letter' is the definition.
(letter from the Greek alphabet)
'king henry beginning to open' is the wordplay.
'king' becomes 'R' (abbreviation of Latin rex).
'henry' becomes 'H' (symbol for the unit of electrical inductance).
'beginning to' indicates taking the first letters.
The first letter of 'open' is 'o'.
'r'+'h'+'o'='RHO'
(Other definitions for rho that I've seen before include "17th Greek letter" , "Greek letter R" , "Seventeenth letter of the Greek alphabet" , "Something like 25 [ETA]" , "Greek letter used as symbol for density" .)