Omabird is right. You will get about half blue palms and half royals.
If you are not familiar with the nomenclature of genetics, royal palms have two black-wing bronze genes, written as b1b1. Each parnet contributes one b1 gene. They also have two palm genes, written cgcg, where each palm gene is one cg. They also have two narragansett genes, each written as ng. Royal palms also have two "not blue" genes, written as dd. So a Royal Palm is b1b1cgcgngngdd.
Blue palms are similar, except they are b1b1cgcgngngDd. They have one blue gene and one not blue gene.
When you breed the two together, the royal pam parent contributes b1cgngd, and the blue palm contributes bicgngD or b1cgngd.
The offspring that get the D from the blue palm parent will look like blue palms and the offspring that get the d from the blue palm parent will look like royal palms.
Birds that are b1b1cgcgngngDD are also called blue palms (See Porter's heritage turkeys website). If these breed with royal palms, all the offspring will have Dd, and look like blue palms.