Express horror during prank that terrifies animals (8)

I believe the answer is:

staghunt

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'terrifies animals' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.

'express horror during prank' is the wordplay.
'express horror' becomes 'agh' (I can't justify this - if you can you should believe this answer much more).
'during' indicates putting letters inside.
'prank' becomes 'stunt' (I've seen this in another clue).
'agh' inserted into 'stunt' is 'STAGHUNT'.

'that' is the link.

Can you help me to learn more?

I've seen this clue in The Irish Times.

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