Do you have your save files stored locally or on the cloud? If the save files are stored locally, there should be an option to import them to your Enhanced Edition game. However, if your old save files were stored on the cloud, the Enhanced Edition will not let you import them. In that case your option is to install your old vanilla version of DL again and download the save files from the cloud first and then update to the Enhanced Edition.
Alternatively, you can use the Share Play function. If you start Share Play at the PSN Party, you will be able to control another player's game (one which also has the old version of the disc). After playing, you should have the symbol of the old game in the PS4 menu.
Then, you should be able to download the old save data from the PSN online storage. The system is going to think you have the old version of the disc too. As a result, you will be able to transfer your data to the hard drive.
If the above methods fail, try restoring your console's licenses: Select PlayStation Network/Account Management and then Restore Licenses. Having done that, sign out of your PSN profile and sign back in.
If that does not help, delete the game completely and re-install it, making sure you have stable internet connection during and after the installation process, so that the game's large critical update can be downloaded and successfully applied.
In order for the game to download completely, with all the additional content and updates, please make sure that you do not turn the console completely off. Instead, go to Settings -> Network -> and tick the Connect to the internet option. Then, go one step back and enter Power Save Settings. Having entered these settings, choose Set Functions Available in Rest Mode and tick the Stay Connected to the Internet option. Having done all that, when you try to turn the console off, you will have the Enter Rest Mode option available. Select this option, please.
Having performed the above steps, there should be an option to import your old save files in the "Play Game" menu.
Please NOTE that the issue can also stem from your previous product and the Enhanced Edition's regions.
See: Disc REGION issues