Awfully real King in a play of Shakespeare (4,4)

I believe the answer is:

king lear

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

'play of shakespeare' is the definition.
'King Lear' can be an answer for 'play' (Shakespeare play). I'm unsure of the 'of shakespeare' bit.

'awfully real king' is the wordplay.
'awfully' is an anagram indicator.
'real'+'king'='realking'
'realking' is an anagram of 'KING LEAR'.

'in a' acts as a link.

Can you help me to learn more?

(Other definitions for king lear that I've seen before include "Shakespearian royal tragedy" , "drama" , "One of Shakespeare's tragedies" , "Tragic Shakespearean monarch" , "Play set in medieval Britain" .)

I've seen this clue in the Sydney Morning Herald.

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