She is old but still has (full) 'possession' of her senses/faculties. [=she is still able to think clearly]
I have 'in my possession' [=I possess] silverware that has been passed down in my family for generations.
He did not have 'possession' of the ball before he was knocked out of bounds.
(..) ...I didn't think he'd really do it. Gandalf? Bilbo's ring. He's gone to stay with the Elves. He's left you Bag End. AIong with all his possessions. The ring is yours now. -Put it somewhere out of sight. -Where are you going? -There are some things that I must see to. -What things? (..)2001 The Lord of the Rings: The Fellowship of the Ring