Many airlines in Europe and the United States of America have hoped that the Biden government will ease their entry requirements quickly. Nothing seems to come of this, at least in the short term.
In any case, it is certain that in the future the full vaccination against Covid-19 will be a basic requirement for entry. The Travel Ban for EU citizens and other states in Europe, which was enacted under Donald Trump, has not yet been lifted. Nothing about that will change in the short term.
The US government does not intend to relax before the end of November 2021. As a possible date, there is a vague prospect that there could be gradual openings after Thanksgiving. This has been heavily criticized by airlines on both sides of the Atlantic. Immediate opening is requested for fully vaccinated people.