Does a dragon's Star Rank reset every reign?

No. Star Rank is 100% permanent. It never resets and carries over between reigns (8-week reigns). That's what makes it one of the safest pillars of your progression.

Don't confuse it with the dragon's level (Reign Level), which does reset every season and has to be re-ground. So:

• Stars = permanent capital (keep it, stack it, nothing to fear)
• Level = throwaway (raised again each reign through combat or meat)

Simple rule: everything you put into relics → stars is won for good. If you're unsure where to put your effort at the end of a reign, stars are always a good pick because they go through the wipe.