Nero, for instance, was in a right state! (5)

I believe the answer is:

roman

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'nero for instance was' is the definition.
I can't tell whether this defines the answer.

'right state' is the wordplay.
'right' becomes 'r' (common abbreviation).
'state' becomes 'oman' (Oman is a country).
'r'+'oman'='ROMAN'

'in a' acts as a link.

Can you help me to learn more?

(Other definitions for roman that I've seen before include "Like the English alphabet" , "Locking device" , "Classical" , "Latin" , "Citizen of Italian capital" .)

I've seen this clue in the Evening Standard.

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