I have a porcelain veneer and the tooth has a cavity. Do I have to get a new veneer after the cavity is filled?

Veneers that are covering the tooth can not cavity, but your tooth that is supporting the veneer can get cavity.
In most cases the veneer can be saved by removal of the cavity and bonding the filling to the existing tooth. Depending on where the cavity is, the dentist and you will make a decision if it can be blended or you need to redo your veneer. Usually if the cavity is from the palatal side, or lingual side and the xtent of cavity is not large, you can salvage the veneer.

Thanks for asking the question. Well, that totally depends upon the tooth cavity. If the cavity is minor and veneers is not affected with it then your dentist will clean the tooth and use the older veneer otherwise you need new one after tooth filling.

Often, the decay can be removed and the cavity filled with a white filling material that blends with the veneer. No guarantee, but often we can do this. Hopefully, your cavity is small enough for it to go this way.