In political science, a proxy war is an armed conflict where at least one of the belligerents is directed or supported by an external third-party power. In the term proxy war, a belligerent with external support is the proxy; both belligerents in a proxy war can be considered proxies if both are receiving foreign military aid from a third party country. Acting either as a nation-state government or as a conventional force, a proxy belligerent acts in behalf of a third-party state sponsor.[1]

That’s a very loose definition of a proxy war, by that metric basically any war since globalisation is a proxy war.