In support of backing the ruling head (3)
I believe the answer is:
for
This could be a double definition.
'in support of' is the first definition.
(as in being for a particular cause)
'backing the ruling head' is the second definition.
'for' can be an answer for 'backing' (I've seen this in another clue). I am not sure about the 'the ruling head' bit.
Can you help me to learn more?
(Other definitions for for that I've seen before include "On behalf of" , "Favouring" , "In support of" , "On the side of" , "See 24" .)