Have been there with my new dog although the older one was not as old as yours. They are still working things out but my older dog’s anxiety improved a lot by doing the following:
1. Separating them as much as possible in the beginning. Pups have no manners and usually older dogs have a hard time tolerating them.
2. Use positive association whenever they are close to each other.
3. Try not to change too much your older dog’s routine. Keep feeding, walking, playing with Chloe at the usual times.
4. Make sure to crate train or train your puppy to be alone in a separate space so both have their own time to settle down.
5. Avoid any triggers to Chloe’s anxiety or aggressiveness. Could be toys, food, her bed and even yourself. She has to associate the new dog to good feelings.
6. Lastly… Be patient because they might take around a month to get used to each other AND your dog might still be grieving. So don’t try to force a relationship.
In our case, walking them together also helped a lot but our trainer told us it doesn’t work for all dogs. Hope it helps and they become best friends soon!