Hannah is Clarissa's girl. Yeah, it probably wasn't the smartest idea to take lovers' letters back and forth when Clarissa's already in hot water with the fam. But Hannah is so loyal to her mistress, she'll do anything to keep her happy—while she's in the family's service, that is.
Hannah definitely loves Clarissa, but it's doubtful how far she'll go to help her after The Event. When Clarissa writes to beg for help, Hannah sends this dubious response: "I have not forgot to write, and never will forget anything you, my dear young lad, was so good as to larn me" (299.1). There's definitely a "but" coming: "I am very sorry I cannot come to do you love and service" (299.1). Unfortunately, Hannah has to look out for number one.