I think you could also just start a new career, otherwise you should compete in the series that comes after the season and then the contracts starts rolling in. I started with the Clio Challenge, had to compete in the Classic Touring series and then got offerings from teams from Formula 1000 and the GT5 Ginetta G40 Challenge. 👍
But, if you want to start in the GT3, I think the easiest and quickest way would be to just start a new career, I think you can start directly from the GT3.