Old cat harassed by new puppy

Ever since I brought my puppy home (4 months ago), she's been quite enthusiastic towards the cat (which isn't very nice/friendly/interested with the puppy).

Puppy wants you to play, and gets in the cat's space a lot to the point that the cat has stopped coming into the living room (where the puppy is baby gated most of the time). She used to snuggle on the couch with me all the time, but now she keeps away.

I'm wondering if they'll ever be able to cohabit? I protect the cat a lot. She's 9 and she's scared of my puppy because she's so huge already (6 months – 45lbs/20kg).

The puppy isn't scared of the cat hissing at her or the smacks on the nose. She keeps insisting and I have to walk in, body block the dog and point her in another direction ("out"), which only builds her frustration and doesn't discourage her to repeat the behaviour a little later in the day or whenever the cat builds up the courage to come in the living room.

Anyone had a similar experience? I don't want my cat to be alone all the time. Feeling bad for her and wondering if there's anything I could do to make my puppy understand to leave the cat alone.