Yes—the Nikon 300mm f/4 AF-S is generally a strong match for the D7000 for sports and wildlife, and it should be much sharper and more suitable than an 18-200mm at the long end. A 300mm prime gives you better optical quality and a faster maximum aperture than superzooms, which helps for action and distant subjects.

The D7000 can use that lens, and the 1.4x teleconverter combination is commonly considered, but adding the teleconverter reduces the maximum aperture from f/4 to f/5.6. That can make it less ideal for fast action or low light.

If you regularly need more reach for birds or small wildlife, 300mm may still feel short, and faster/larger pro telephotos are often preferred—but those are typically much more expensive and heavier.

Practical advice from the community: if possible, rent or borrow a long lens first to confirm whether 300mm is enough for your subjects. Also, for wildlife especially, getting closer can matter as much as buying more focal length. Overall, the 300mm f/4 is a very good value choice if you want a sharp, capable telephoto for the D7000.