Responsibility of old star from the east (4)
I believe the answer is:
onus
'responsibility' is the definition.
(onus is a duty or responsibility)
'old star from the east' is the wordplay.
'old' becomes 'o' (abbreviation as in OT - Old Testament).
'star' becomes 'sun' (the Sun is a star).
'from the east' says the letters should be written in reverse (on a map from right to left).
'sun' reversed gives 'nus'.
'o'+'nus'='ONUS'
'of' is the link.
(Other definitions for onus that I've seen before include "'Burden, load (4)'" , "Obligation - charge" , "Duty or responsibility" , "'Burden, of proof (4)'" , "Liability" .)