Board Thread:Questions and Answers/@comment-7278867-20170422143147/@comment-32563139-20170713091509

As he has royal blood, Zeke CAN use the founding titan, but he'd have to retrieve it from Eren, who currently has it. However, if Zeke dies before he could get it... Zeke could have children and they'd posess royal blood, but I think it's unlikely. On the other hand, Historia (Krista) has royal blood, so if she, or maybe her future child, was injected with the titan serum, to eat Eren (possibly near to the end of his 13 years) that would mean the Eldians had the power of the founding titan, and they could actually use it.

Eren can't use it right now because he does not have royal blood, he could only use the co-ordinate ability because he had just made contact with Dina Frits' titan form, Dina has royal blood.