The phrase "predominant role" means that something or someone is the most important or influential in a particular situation or context. Full definition
Moreover, the demand for this precious metal in Chennai is mounting owing to its symbolic value, and predominant role in South Indian traditions and weddings. (policybazaar.com)
And so today, even in some of Jack Tilton's shows where they have maybe twenty pictures of a black guy showing his butt, or when they had that show Black Male: Representations of Masculinity in Contemporary American Art [at the Whitney Museum of American Art in» 94], where the gay element had a more predominant role — I mean, it was first brought into the scene with Lyle Ashton Harris having that show [Face: Lyle Ashton Harris at the New Museum in» 93]. (bombmagazine.org)
I was unsure if I should include the Olympic Games series, but Sonic and friends have predominant roles in the, uh, Olympic proceedings, so here we are. (segadoes.com)