The most common and most likely answer to this crossword clue is the 6 letter word GRANNY
I've seen this crossword clue in Independent
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Buddy explains!

The straight part
We know that "older lady" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case older lady = granny.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GRANNY mean?
GRANNY noun- A grandmother.
- An elderly woman.
- (knots) A granny knot.
- (farming) An older ewe that may lure a lamb away from its mother.
- To be a grandmother.
- To act like a stereotypical grandmother; to fuss.
- Typically or stereotypically old-fashioned, especially in clothing and accessories worn by or associated with elderly women.