Responsibility for returning some letters unopened (4)
I believe the answer is:
onus
'responsibility' is the definition.
(onus is a duty or responsibility)
'returning some letters unopened' is the wordplay.
'returning' is a reversal indicator.
'some' indicates a hidden word (some of the parts of the word are used).
'suno' can be found hidden inside 'letters unopened'.
'suno' back-to-front is 'ONUS'.
'for' acts as a link.
(Other definitions for onus that I've seen before include "Burden, duty" , "'Burden, of proof (4)'" , "albatross?" , "'Responsibility, task or burden (4)'" , "Weight of responsibility" .)