Is there a career mode in Forza 6 Apex? If so, how to start it?
Forza Motorsport 6: Apex is a slimmed down version of the larger Forza Motorsport 6 which had a career mode.
Unfortunately this game, being a slimmer version, does not have what you are expecting.
The only thing that you can find a little similar to the career mode are the 12 different events on a kind of a racing calendar (first menu button with recommended events)
More information about the game and menu:
https://gamingbolt.com/forza-motorsport-6-apex-wiki https://forums.forzamotorsport.net/turn10_postsm469206_Forza-Motorsport-6--Apex-quick-facts-and-FAQ.aspx#post_469206