If I backup my PS4 games to a HDD, can I move them to a new PS4?

I want to put my games onto a HDD and sell my PS4, but keep them there if I buy a PS4 ever in the future. Is this possible? Just I do not want to lose the games you can no longer download any more like P.T. However since I'm moving a long distance I cannot carry anything big with me like a PS4.

Just I remember before trying to do this when I upgraded to a Pro and it said the games were locked to my previous console.

Thanks.