"Because the service of the holy belongs to them, they shall bear upon their shoulders"—Numbers 7:9.
The kohanim (priests) are commanded to carry the Ark [containing the Tablets] on their shoulders—when necessary to transport it from one location to another.
Although the Levites were originally entrusted with this task, this was only in the desert, when the kohanim population was very small. But in all future generations, this is a task reserved for the kohanim.