How do i get a purchased app onto my icloud?

About a year ago i switched from my dad’s apple id to my own. Unfortunately some of my purchased apps that i got before my switch didn’t sync with my icloud. it wasn’t really an issue until i got a new ipad. now it says i can’t get the apps i previously purchased for free. i think that if i find a way to sync my purchased apps with my icloud properly then it might work. is there any way to do this?