What was the relationship between Hannah and Mary?
The Catechism says that some holy women prepared for Mary’s mission. It names Hannah, the mother of Samuel. 1 Samuel 1:11, 20; Luke 1:38
What the Bible says
1 Samuel 1:20
And it came to pass when the time was come about, Anna conceived and bore a son, and called his name Samuel: because she had asked him of the Lord.
Luke 1:38
And Mary said: Behold the handmaid of the Lord; be it done to me according to thy word. And the angel departed from her.
Douay-Rheims Bible (Challoner revision), public domain.
What the Church teaches
The Catechism names Hannah among the women who kept alive the hope of Israel. The purest figure among them is Mary.
Catechism 64 · Catechism of the Catholic Church