When ground beef is fresh it will be a brighter red color and as it's going bad it starts to turn brown or gray in color bu that doesn't mean it's bad and unsafe to eat.
Even gray colored or brown ground beef can be okay and safe to eat as long as it's been frozen but it just won't be as fresh tasting.
But if the ground beef has a bad odor to it or it's becoming slimy or feels sticky then it's bad and should be thrown out.
If you keep the ground beef frozen it should last 6 months to a year before going bad.