Crossword Genius

Possible carrier’s responsibility? (6)

Ross

I believe the answer is:

pigeon

I'm a little stuck... Click here to teach me more about this clue!

'carrier's responsibility?' is the definition.
Although both the answer and definition are singular nouns, I cannot see how one could define the other.

'possible' is the wordplay.
I cannot quite see how this works, but
'possible' could be 'on' ('not on' can mean unacceptable or not possible) and 'on' is present in the answer.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for pigeon that I've seen before include "One pig for the bird" , "Common dove" , "Go pine for the bird" , "Common city bird" , "Common bird, wild and domesticated" .)

I've seen this clue in The Times.
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