“From Omicron?”
Yes. Somewhat less than other variants, and differing in the protection levels against infection (least), severe disease, hospitalization and death (most). Significant protection from hospitalization and death.
“For how long?”
TBD. Some vaccines wane in effectiveness more than others. Natural immunity also tends to wane over time in other coronaviruses (typically a few months to a few years).
RE: TBD
A report from a study tells us 10 weeks. See here:
Then what? Another booster?
As for natural immunity, studies show that on average it lasts for years ( and counting ). See here:
Studies from the Cleveland Clinic and several in Israel tell us the natural immunity is superior compared to those of any vaccine. Here’s one for instance:
https://www.medrxiv.org/content/10.1101/2021.08.24.21262415v1
And here: