Thesp’s last amateur theatre piece? (4)

I believe the answer is:

play

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'theatre piece?' is the definition.
'play' can be an answer for 'piece?' (thesaurus). I'm not sure about the 'theatre' bit.

'thesp's last amateur' is the wordplay.
'last' says to take the final letters.
'amateur' becomes 'lay' (similar in meaning).
The last letter of 'thesp' is 'p'.
'p'+'lay'='PLAY'

Can you help me to learn more?

(Other definitions for play that I've seen before include "Participate in games or sport" , "Hamlet, for example" , "Stage drama" , "Drama - latitude - sport" , "Drama; engage in games" .)

I've seen this clue in The Times.

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