Recently, Sony removed the ability to move PS3 worlds to PS4 with the in-game converter.
Don't worry, you can still do it (and now directly to PS5) thanks to the Universal Minecraft Tool!
Your PS3 worlds will work great on PS4 or PS5, but they will be on the Bedrock edition, not the Legacy Console edition. If you are okay with this, let's get started!
To begin, you'll need to tell to the UMT which world you're trying to convert.
Follow this guide to Open a PS3 World in the Universal Minecraft Tool
Click Bedrock to select it as the target output edition.
You'll notice a drop-down menu for selecting different target versions. This can be useful if you're trying to get more advanced with your world conversion, but for most cases you'll want to leave it on the latest version.
For reference: Minecraft PlayStation 3 edition never made it past 1.6.0 Bedrock equivalent.
Click Next to continue.
This panel allows you to control certain technical aspects of how the conversion should run. Thankfully, for PS3 to Bedrock conversion you'll usually want to leave these at their default values.
One very important setting you'll likely want to keep enabled is the Allow Older Chunk Versions feature. It is crucial to ensuring you don't have any holes or empty spots in your world.
It's the big moment!
Click Start Conversion to begin.
The UMT will now scan the input world and perform all the necessary conversion steps to create a super-accurate clone of your world for Bedrock edition.
After conversion, pick a spot to save the output world.
Click Save World to bring up the save window.
The UMT will default to the install location of your Windows 10 edition worlds. You will need Minecraft Windows 10 edition installed in order to transfer the world in the next step with Realms.
Enter a name for the world, and click Save.
You'll need a Realms Plus subscription to move your world from Minecraft Windows 10 edition to your PS4 or PS5 console.
The free trial of Realms Plus will work, thankfully!
Plus, having a Realms server is super handy, or you can always cancel your subscription if you choose not to continue.
Click the Realms Plus banner near the top of the main menu.
Start a free trial of Realms Plus.
You should see your Realms server activated where the banner used to be.
Click Edit on your Realms server.
Click Edit World in the Ready to Play section.
On the right settings panel, scroll all the way down and choose Upload World.
Choose the world we just converted earlier.
Head on over to Minecraft on your PS4 or PS5 console.
Make sure you are signed into the same account you purchased Realms with!
Head back into the same page where you uploaded the world, except this time we'll download it.
On the right settings panel, scroll all the way down and choose Download World.
Congratulations! You've successfully converted and transferred the world!
Let the Universal Minecraft Tool simplify your life. Accomplish your tasks now.