Coffindaffer, Rebecca. Crownchasers #1

Series information from Goodreads

A deadly race across 1,001 planets will determine more than just the fate of the empire. Alyssa Farshot has spent her whole life trying to outrun her family legacy, even leaving behind the Kingship and her uncle, the emperor, for a life of exploring. But when her dying uncle announces a crownchase—a search for the royal seal hidden in the empire that will determine the next ruler—Alyssa is thrust into her greatest, most dangerous adventure yet