Will my progress be saved if I uninstall a digital game from my PS4?

Solution 1:

Yes, if you delete a game from your PS4, you will have access to your old save file whenever you choose to reinstall it.

I recently reinstalled God Eater 2 after playing nearly a year ago and my save file was accessible (though I opted to create a new file, because I did not remember where I was in the story).