It is possible to increase the size of an existing RAID set. But it has it's drawbacks....
Basically you buy all drives you need to replace the entire set.
Take out one drive, replace it with a new one and let it rebuild. Depending on the size your RAID set this can take a few hours to days.
Rinse and repeat until everything has been replaced.
Most likely the RAID software did not automatically detect the increase in size so you will have to enter the RAID configuration software to increase the size of the set.
This solution works great it if you for some reason can't afford downtime.
The biggest drawback on this solution the time it takes to restore, the performance hit and the risk it imposes depending on the RAID configuration.
Obviously large datasets take DAYS to restore and rebuilding eats up a lot of processing power.
The risks however, if you do this with a RAID 1 or 5 set, you can only lose one disk. This means if during a rebuild another disk fails due to the amount of read/writing it has to do, you will lose your set. The risk is less if doing it with a RAID 6 set.
If you have the choice, it's recommended to completely delete the existing set and make a new one and restore the files from backup.
It will take way less time and the risk is significantly smaller.