Save data for Monster Hunter: World is stored locally on the PlayStation 4 hard drive. In the event you are a PlayStation Plus user, and Automatic Upload was enabled and your save data was uploaded to the cloud prior to save data deletion, you can try downloading the uploaded save data from the Cloud and continue from that data.
To do this, perform the following steps:
Select your local user and go to [Settings] > [Application Saved Data Management] > [Saved Data in Online Storage] > [Download to System Storage].
Choose the game saves you want and select download.
If there is only older save data present, and a more recent save was not backed up in the cloud or on a USB drive prior to deletion, then there would be no way to restore this data. Save data for the game is only stored locally on the PS4 hard drive and/or the PlayStation Plus cloud, and not on the Monster Hunter: World servers. Capcom is unable to provide nor create save data in the event a user's save data is lost.