He could take the principle of Young Apprentice and tweak it elsewhere I guess if other channels were interested, but The Apprentice rights belongs to the BBC not Lord Sugar.
Surprisingly, Lord Sugar appears to have a huge amount of the decision-making power himself. It was apparently him that decided to change the name of Junior Apprentice
to Young Apprentice
because apparently 'they're not junior to anyone'. It was also apparently him who demanded that the format change from Series 3 onwards so that he could fire more than one person (after the fiasco with the chickens in Series 2 when he wanted to fire Alexa and Syed, but could only fire one of them), and he who changed it from a job to a business opportunity.
I'm not sure how he manages all this, but I think it's possible that he has Mark Burnett on his side, who owns the entire Apprentice
franchise. Maybe Mark Burnett can overrule the BBC and take it to another channel? I don't know exactly how it works, but from what he says, Sugar is apparently able to take his contract wherever he likes.