You can only start a star player career mode as an international player. Aka players listed in the in-game 35-man squads of the full member nations (the 9 countries apart of the World Test Championship).
Unfortunately you can't start a star player career mode as a domestic player, say you wanted to start a star player career as Nic Maddinson for Victoria, the only way you could do this is if you added him to the Australian squad in the Academy beforehand. Likewise, if you want to start a career mode directly in domestic cricket instead of playing through club cricket, there is no way to do this.