Crossword Genius

Hockey venue that's 'horrible', girl admitted (3,4)

Ross

I believe the answer is:

ice rink

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

'horrible girl admitted' is the definition.
I can't tell whether this defines the answer.

'hockey venue' is the wordplay.
'hockey' becomes 'ice hockey' (synonyms).
'venue' becomes 'rink' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'ice'+'rink'='ICE-RINK'

'that's' is the link.

Can you help me to learn more?

(Other definitions for ice rink that I've seen before include "Skating arena" , "Place to skate" , "Place for skating" .)

I've seen this clue in The Independent.
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