The phrase "to edge out" means to gradually overcome or surpass someone or something, often through a series of small advantages or gains. Full definition
Despite any PR by major publishers, we're being slowly edged out of a hobby a lot of us came up in and it's just something you have to be okay with. (gameological.com)
Don't be discouraged if you get edged out by another buyer. (homeownership.ca)
The duo whose nominations brought great joy and press coverage of the Nigerian music industry, were edged out in their respective categories, as they failed to pick up any award. (nigeriapoliticsonline.com)