Answer:
She did a number of things. Such as putting her on house arrest, keeping her in isolation, allowing her no vistors. Eventually signing her death warrant, charging her for treason, which led to her execution. She moved her to many different castles as Mary was involved in many plots against Elizabeth too etc.
Though point to note, Mary was against her charge of treason claiming she wasn't a English subject but a Scottish one, hence she couldn't be charged for treason (she still got charged foe it though).