Play to see, with Rex in it (5)

I believe the answer is:

sport

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'play' is the definition.
(I know that play can be written as sport)

'see with rex in it' is the wordplay.
'see with' becomes 'spot' (to spot is to notice or catch sight of. I am not sure about the 'with' bit.).
'rex' becomes 'R' (abbreviation e.g. GR=George Rex, King George).
'in it' means one lot of letters goes inside another.
'spot' enclosing 'r' is 'SPORT'.

'to' acts as a link.

Can you help me to learn more?

(Other definitions for sport that I've seen before include "Game; display" , "entertainment" , "eg Tennis" , "Show off" , "Fun; wear" .)

I've seen this clue in The Guardian.

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