I'll give a real world answer here since I'm a sheriff's deputy in Florida (thus my response will pertain to Florida statutes, FYI).
A suspended or revoked license is a bit different than an expired license. Suspended/revoked came from a court order, thus on a traffic stop I will either arrest them or give them a mandatory court date if another licensed citizen is able to drive the vehicle. This usually entails a quick call to the state attorney's office or my supervisor, but generally our agency policy is to make the arrest. To liken this to GTA, the most realistic scenario would be to arrest the driver.
Now, an expired license is one that has simply not be renewed following its expiration date. In the state of Florida, there are various statutes I can apply in this situation. If the license has been expired less than 90 days, I can write them a citation (similar to a fix-it ticket), where they have a certain number of days to go renew in order to have their fine reduced to an administrative fee. If over 90 days, it is treated like a suspended/revoked license as mentioned above.
So ultimately from a realism perspective, you can role play and decide how to handle it. If you want to follow the idea that the license is actually revoked by the courts, then make the arrest. If you want to assume it expired yesterday and they forgot to get it renewed, write the citation.