Eastern ruler open to the west (4)
I believe the answer is:
raja
'eastern ruler' is the definition.
'open to the west' is the wordplay.
'open' becomes 'ajar' ('ajar' can be similar in meaning to 'open').
'to the west' says the letters should be written in reverse.
'ajar' backwards is 'RAJA'.
(Other definitions for raja that I've seen before include "Indian ruler" , "sovereign" , "Indian prince or king" , "Asian prince or king" , "Prominent Indian" .)