"To claim the crown" means to assert one's right or make a formal declaration to become the ruler or monarch of a certain kingdom or domain. Full definition
The company might easily claim the crown in the cable TV realm. (finder.com)
And he would be able to avoid asking questions from reporters — again — until he arrives to claim his crown at the convention. (nystateofpolitics.com)
Expanses of connected fungi or coral can also claim the crown of world's largest life form, and single - celled animals can reach surprising sizes. (newscientist.com)