Noble American maiden lady, rather old (7)

I believe the answer is:

grandam

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

'lady rather old' is the definition.
I can't tell whether this definition defines the answer.

'noble american maiden' is the wordplay.
'noble' becomes 'grand' (similar in meaning).
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'maiden' becomes 'm' (cricket abbreviation).
'grand'+'a'+'m'='GRANDAM'

Can you help me to learn more?

(Another definition for grandam that I've seen is " Experienced old woman".)

I've seen this clue in The Independent.

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