Hi
The trick to get this achievement, as on the previous F1 games, is to make a backup save (in the cloud, for example), when you get the email with the contract offer.
I started a Long Career Championship, and I chose Mercedes. You can pick whatever team makes your fancy, but the game is easier with either Mercedes or Red Bull.
At the end of the German Grand Prix, the 10th race, after winning every race up to then, I received a contract offer from Ferrari. I backed out of the career menu, went to "My F1", then saved on the cloud, thus creating a backup save. I saved again on my HDD, then went back to Career, accepted the contract, got the achievement, then I went to the dashboard.
I restarted the game, picked up cloud as my save, checked if I was still with Mercedes, saved on my HDD, then carried on with the game.
Nice and easy.