Went out, having agreed to leaving (6,3)

I believe the answer is:

nodded off

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'went out' is the definition.
Although both the answer and definition are past participle verbs, I cannot understand how they can define each other.

'agreed to leaving' is the wordplay.
'agreed' becomes 'nodded' (I've seen this in another clue).
'to leaving' becomes 'off' (as in 'I'm off').
'nodded'+'off'='NODDED OFF'

'having' is the link.

Can you help me to learn more?

(Other definitions for nodded off that I've seen before include "dozed" , "Fell asleep" .)

I've seen this clue in The Daily Express.

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