you have a good chance that you will need a new Brake drum pistons on such an old model, they will fail eventually. its better to get a new pair(for both sides), so you have evenly matched brake function.
Always change brake parts in axle pairs, (drums, pads, Drum Pistons/Calipers, handbrake cables) to ensure you dont get the other side suddenly fail after you had the original fault on the other side fixed.
a failure of one rear brake will result in the car skidding out of control if braking on a corner or it pulling excessivly to one side and the risk of skidding when braking in a straight line. (especially in the wet)
if its drum brakes you will need to release the handbrake cables and dismantle the drums to reset the auto-adjusters. clean them up, dont use grease or
on the mechnaism. reassemble and refit the handbrake cables, adjust the central aduster to get even tension then use the brakes to get the slack taken up by the autoadjuster.
brake bite should not occur untill click 3(free brakes up to 3) and full lock at click 8 of the handbrake.
if you cannot get it to autoadjust or even braking then replace the handbrake cables and consider replaceing the brake adjuster if the internal springs are faulty (you can get repair kits for drums)
when finished, take the car to a MOT station for brake safety check (FREE)