You can reuse it for 'refrigerator pickles', but as the name implies, these are made and then stay in the fridge and get eaten within weeks.
One easy, 'cheat's pickle' uses cucumber slices, brined with a couple of table spoons of salt in a large bowl, topped with ice cubes, covered with an upturned plate. After 3 hours, wash, then drain cucumber slices very well and place them in jars and top with the old pickling vinegar. Slices must be covered by the solution. After 3 days in the fridge, the 'cheat's pickled cucumber' is ready to eat.