In ancient Rome, holding a priesthood was more like holding a government office than having any personal calling to the religious order. There were several colleges (groups) of priests who would have official government duties and functions. Often Roman men would go from political office to the priesthood and vice versa.
As an example, I bring you this dedication (not a tombstone!) to the duty/responsibly of Gaius Calvisius Sabinus found in the Museo Civico di Spoleto.
[C(ai)] CALVISI C(ai) F(ilii) SABINI
VII VIR(i) EPUL(onum) CUR(ionis) MAX(imi)
To the duty
Of Gaius Calvisius Sabinus, son of Gaius
Septemvir of the Epulones and Curio Maximus
Our friend G. Calvisius Sabinus was a patron, which was common in Rome, and a consul. There were two consuls in ancient Rome, who served for one year. Ostensibly, there was a one term limit, but history is filled with exceptions to this rule. Consul was the highest political position one could achieve. G. Calvisius Sabinus tried to save Julius Caesar on that fateful day of March 15th, when his assassins attacked. Because he was consul in 39 BC, it seems that he was given the consulship by the Second Triumvirate as a reward for his loyalty (pietas).
But G. Calvisius Sabinus was also a septemvir epulonum (one of seven men of the epulones) who was in charge of feasts and banquets during public games. He was also the curio maximus, which even Wikipedia calls "obscure." Even so, it was important enough to be an identifying office to the people who made this dedication to him.
This inscription is CIL XI, 4772.