Responsibility assigned to under-secretary (4)
I believe the answer is:
onus
'responsibility' is the definition.
(onus is a duty or responsibility)
'assigned to under-secretary' is the wordplay.
'assigned to' becomes 'on' (I can't justify this - if you can you should believe this answer much more).
'under secretary' becomes 'US' (abbreviation).
'on'+'us'='ONUS'
Can you help me to learn more?
(Other definitions for onus that I've seen before include "Duty or responsibility" , "'Burden, of proof (4)'" , "albatross?" , "'Responsibility, task or burden (4)'" , "'Burden, load (4)'" .)