Responsibility of old star retiring (4)
I believe the answer is:
'responsibility' is the definition.
(onus is a duty or responsibility)
'old star retiring' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'star' becomes 'sun' (the Sun is a star).
'retiring' says the letters should be written backwards.
'sun' reversed gives 'nus'.
'of' is the link.
(Other definitions for onus that I've seen before include "Burden, duty" , "'Responsibility, task or burden (4)'" , "Encumbrance" , "Duty or responsibility" , "Capulet opponent (R&J)" .)