Vaccines considerably bring down the risk of infection. That being said, they do not fully protect you, and given the variants in circulation right now, there’s a high risk that exists for someone who has just been partially vaccinated.
Post full vaccination, when the immunity is said to peak, the risk of infection, as well as outcomes minimize well. From a low risk of hospitalization to severe disease, vaccination can very well save you from a lot of ill-effects. However, there very much is the risk of catching the infection, developing some symptoms is possible and hence, in theory, it is absolutely possible to develop long COVID too.
However, there isn’t evidence-backed data present to determine the risks, and the chances yet.
Despite this, scientists do remain hopeful that COVID vaccines, much like other vaccines, could work their way to reduce the likelihood, duration of symptoms and long-term complications. How well it works is something practically, we’ll only learn in the coming months.