Agitated, having erroneous belief about king (7)

I believe the answer is:

febrile

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'agitated' is the definition.
Although both the answer and definition are adjectives, I can't see how one could define the other.

'erroneous belief about king' is the wordplay.
'erroneous' indicates an anagram.
'about' means one lot of letters goes inside another.
'king' becomes 'r' (r is abbreviation for rex).
'belief' with letters rearranged gives 'febile'.
'febile' going around 'r' is 'FEBRILE'.

'having' acts as a link.

Can you help me to learn more?

(Other definitions for febrile that I've seen before include "Delirious" , "Very hot" , "Unhealthily excited" , "Nervously excited" , "Showing nervous excitement" .)

I've seen this clue in The Times.

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