Fascinatingly alien embraces old monarch in public (8)

I believe the answer is:

exoteric

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

'public' is the definition.
(associated in meaning)

'fascinatingly alien embraces old monarch' is the wordplay.
'fascinatingly alien' becomes 'exotic' (synonyms. I am not sure about the 'fascinatingly' bit.).
'embraces' means one lot of letters goes inside another.
'old monarch' becomes 'ER' (Elizabeth Regina, ie Queen Elizabeth).
'exotic' going around 'er' is 'EXOTERIC'.

'in' acts as a link.

Can you help me to learn more?

(Another definition for exoteric that I've seen is " ordinary".)

I've seen this clue in The Times.

Want a hint initially instead of a full solution? Install my app