Covering up, given royal discomposure (10)

I believe the answer is:

overlaying

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

'covering' is the definition.
(overlaying is a kind of covering)

'up given royal discomposure' is the wordplay.
'given royal' anagrams to 'OVERLAYING'.
Though, I'm not clear how the anagram is indicated.

Can you help me to learn more?

I've seen this clue in The Independent.

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