One creek encircling Ireland's sporting arena (3-4)
I believe the answer is:
ice-rink
'sporting arena' is the definition.
'ice-rink' can be an answer for 'arena'. I'm not sure about the 'sporting' bit.
'one creek encircling ireland's' is the wordplay.
'one creek' becomes 'ick' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'encircling' means one lot of letters goes inside another.
'ireland' becomes 'Erin' (poetic name for Ireland).
'ick' going around 'erin' is 'ICE-RINK'.
Can you help me to learn more?
(Other definitions for ice-rink that I've seen before include "Winter sports arena" , "Place to skate" , "Place for skating" , "Where to find skaters" , "Skating venue" .)