Should They Raise The Driving Up To 21?

YES
1. Cut the number of deaths.
The highest death rate for drivers is amongst the age group 17-25. If the driving age is increased there would be a fall in fatalities arising from motor car use. This has a significant economic benefit.

2. Cut Congestion.
Less drivers on the road will reduce congestion and therefore, reduce costs for firms

3. Reduce Obesity
Driving encourages the population to become lazy and obese. If people can't drive they will be forced to walk, use public transport and cycle. This will help lead to a healthier population, which in turn leads to less strain on the National Health System.

4. Young Drivers overestimate their skill
Young drivers, especially male drivers, are likely to overestimate their ability to drive at speed and in difficult conditions. For people of school age, there is often great peer pressure to drive excessively and in a dangerous way.

Your question is surely asking about Rising Driving Age up to 21. But, you didn't mentioned your country.
Increasing driving age will bring itself some problems.
If you take a look, Teenagers, people between 13-19, are the one who need to travel for their colleges, schools and part time Job offices and even Social Parties etc.
Today, when taxi fares are increasing day by day because of expensive fuel, It can be very difficult for teenagers to afford them because they need to travel extensively during their career building age and taxi fares will result in increasing their expenses to very high extent.