Yes — a polarizer can be used on a 300mm lens, and there’s nothing inherently unsuitable about that focal length. Its effect depends on the light and shooting angle, not on 300mm specifically.

Use it when you want typical polarizer effects: reducing reflections and glare, improving color/contrast, and darkening a blue sky. In fact, telephoto lenses are less prone than wide angles to the uneven or blotchy sky effect that polarizers can cause.

The main tradeoff is the light loss: about 2 stops, which can matter indoors or whenever shutter speed is critical. Since you’re often on a tripod, that may be less of a problem.

One important caution: filter quality matters more on long telephoto lenses. Any optical flaws in a front-mounted filter are more visible because the narrow field of view is magnified across the whole image. So if you use a polarizer on a 300mm lens, it’s worth using a good-quality one.