Just like you don’t need to run 26.2 miles before tackling a marathon, you don’t have to run 13.1 miles in training before a half marathon. The longest long run on most training plans are 10-12 miles (16-19km).
However, you can also go beyond 13 miles in training because you can still recover from runs of that distance quickly, unlike with a full marathon. If you’re an experienced runner, doing training runs of up to 15 miles (24km) to get used to the distance is not uncommon.