Atmospheric nitrogen is removed from the air majorly via nitrogen fixation.
Nitrogen fixation is the process by which nitrogen-fixing bacteria such as Azotobacter, Rhizobium, etc., convert atmospheric N2 into usable nitrogenic compounds such as ammonia, nitrates, etc., which are further used by plants and animals to synthesize essential biomolecules like proteins, nitrogen bases, nucleic acids, etc.
A small amount of nitrogen is also fixed by lightning when high temperatures break N2 bonds to get free nitrogen atoms which react with oxygen creating nitrogen oxides, which can dissolve in moisture to form nitrates.
These nitrates are carried to the surface of the earth via precipitation.