We had a male cat Frankie who we had inherited from my MIL. We had a female named Sassy who really didn't get along with the other cats but for whatever reason, she bonded with Frankie who was also older then her. The 2 of them were able to spend about 6 yrs together before Frankie passed away. Sassy looked everywhere for him. She still refused to have anything to do with the other cats or our dog. I even took her to the vet as she had started to loss weight. The vet said that they grieve the loss of a close companion. It was over 6 months before she even seemed like her old self again.
It might be best to wait awhile before bringing in a new cat if that is what you decide to do.