Herd immunity

Hi guys I understand for our population to get covid herd immunity majority of the population would need to take the vaccine. However, I read that you can still be a carrier with the vaccine and not realize it. If this is true, won’t everyone get covid after the being immunized and not realize it and continue spreading it? Meaning we wouldn’t have heard immunity but it would still be spread without a lot of ppl knowing.

Or, would people no longer become carriers and the virus will slowly go away once ppl are vaccinated?

Plz let me know what you guys think