Busily sit with Cyril being poet? (8)

I believe the answer is:

lyricist

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'being poet?' is the definition.
(thesaurus)

I don't understand how the remainder of the clue works.

(Other definitions for lyricist that I've seen before include "Writer of words, as opposed to music" , "Word-writer for songs" , "Writer of the words of a song" , "Song writer -- it's Cyril (anag)" , "One who writes the words of a song" .)

I've seen this clue in The Telegraph.

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