Discard thoughtfully. Check with local recycling programs if suitable (Nylon is recyclable).
Place the rest of the toothbrush into your compost.
Typically takes 90 days to break down in a commercial compost. You have made the right choice - any way you dispose of this, you can be sure that these toothbrushes will not be land-fill for millions of years to come - unlike many toothbrushes in use today.