Nobody knows yet. It depends on if the circulating virus mutates frequently enough to escape the vaccines.
One of the biggest differences between COVID-19 and the flu is that the latter has a very large animal reservoir, and many of those animals we come into regular contact with. The predominant flu antigens get randomly rearranged amongst migrating bird populations, who pass it on to us and other animals. As far as we know, there is no large animal reservoir of SARS-CoV-2. The closest animal analog comes from a specific bat population, but there's sufficient genetic difference between this bat virus and SARS-CoV-2 that it may have needed to mutate first in a human or another animal intermediary host before it could spread among humans. So, the virus jumping between species may have been a one-off accident. Along this theory, if we kill it in humans, it goes away altogether, like SARS-CoV-1.
This is why it is so important to go all-in NOW to drive cases into the ground. Minimize its chances to infect new hosts, and don't give it enough opportunities to mutate away from the vaccine coverage.