Get calm fast, if cuddled (6)

I believe the answer is:

pacify

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'get calm' is the definition.
I can't tell whether this defines the answer.

'fast if cuddled' is the wordplay.
'fast' becomes 'pacy' (I've seen this before).
'cuddled' means one lot of letters goes inside another.
'pacy' going around 'if' is 'PACIFY'.

Can you help me to learn more?

(Other definitions for pacify that I've seen before include "Make calm, appease" , "Quieten" , "Soothe - appease" , "Mollify, appease" , "Make calm, soothe" .)

I've seen this clue in The Sun.

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