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Responsibility assigned to under-secretary (4)

Ross

I believe the answer is:

onus

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'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)'" .)

I've seen this clue in The Times.
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