Over-60s righted a wrong (5,3)

I believe the answer is:

third age

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'over-60s' is the definition.
I can't tell whether this defines the answer.

'righted a wrong' is the wordplay.
'wrong' is an anagram indicator.
'righted'+'a'='righteda'
'righteda' is an anagram of 'THIRD AGE'.

Can you help me to learn more?

(Other definitions for third age that I've seen before include "elderly group" , "period for retirement activity" , "Old people collectively" .)

I've seen this clue in The Times.

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