The most common and most likely answer to this crossword clue is the 6 letter word WITHER
I've seen this crossword clue in Financial Times
W
I
T
H
E
R
More clues leading to the result WITHER
- Shrink from someone trying to be funny — that woman!
- Shrivel up in old age, like queen’s consort?
- Shrink uses humour on woman
- Shrivel up in the company of Her Majesty
- Humour woman or perish
- Become parched accompanying the Queen
- After onset of winter their nuts shrivel up
- Shrivel up accompanied by the monarch
- Having little hesitation to decline
- Sharpness of woman’s buckle
Buddy explains!

The straight part
We know that "Shrivel up in old age" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shrivel up in old age = wither.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 WITHER mean?
WITHER verb- To shrivel, droop or dry up, especially from lack of water.
- To cause to shrivel or dry up.
- To lose vigour or power; to languish; to pass away.
- To become helpless due to emotion.
- To make helpless due to emotion.
- Against, in opposition to.
- To go against, resist; oppose.