Demonstration about court case kept short for senior woman (9)
I believe the answer is:
matriarch
'woman' is the definition.
(I know that matriarch is a type of woman)
'demonstration about court case kept' is the wordplay.
'demonstration' becomes 'march' (type of protest or demonstration).
'about court case' becomes 'atri' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'kept' is an insertion indicator.
'march' enclosing 'atri' is 'MATRIARCH'.
'short for senior' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for matriarch that I've seen before include "Woman dominating" , "venerable old lady" , "Dominant female" , "Very old or venerable woman" , "Female head of a family or tribe" .)