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With leader demoted, nation cheers royal with great care (13)

Ross

I believe the answer is:

painstakingly

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'with leader demoted nation' is the definition.
I can't tell whether this defines the answer.

'cheers royal with great care' is the wordplay.
'cheers' becomes 'ta' (both can informally mean thank you).
'royal' becomes 'kingly'.
'with' says to put letters next to each other.
'great care' becomes 'pains' (I've seen this in another clue).
'ta'+'kingly'='takingly'
'takingly' after 'pains' is 'PAINSTAKINGLY'.

Can you help me to learn more?

(Other definitions for painstakingly that I've seen before include "with great care" , "In a most careful way" , "In meticulous style" .)

I've seen this clue in The Times.
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