The phrase "to eliminate the competition" means getting rid of or removing other people or companies that are trying to achieve the same goal or succeed in the same area as you. Full definition
I think it's a whole strategy to become # 1 by eliminating the competition. (kaitnolan.com)
First, we need to eliminate the competition among ourselves. (edutopia.org)
He put forward the idea of having one exam board for each subject, which he argued would eliminate this competition between boards and provide more consistency of grades. (educationbusinessuk.net)