[Greg67]

False
There is no specific immunity to a new virus. After recovery from one you get specific immunity. In some cases in others T cell memory is gained.

There is natural unspecific immunity that makes one survive a new virus. Without it any new virus can wipe a any species.

[Kartographer]

The immune systems of more than 95% of people who recovered from COVID-19 had durable memories of the virus up to eight months after infection.
The results provide hope that people receiving SARS-CoV-2 vaccines will develop similar lasting immune memories after vaccination.

https://www.nih.gov/news-events/nih-research-matters/lasting-immunity-found-after-recovery-covid-19