Can elderly get pneumonia vaccination after recovery from pneumonia?

Yes. But understand the limits of its effectiveness. This shot helps you develop protective antibodies to strains of bacteria that are included in the shot. It does not stop all potential germ causes of pneumonia. I do find it valuable & got it myself.

It is useful to get vaccine for pneumonia, If the person has not taken Covid vaccine, s/he do that too. A person over 50 years of age should also get Shingles vaccine. It would prudent to renew other vaccinations as well, e.g., DPT.