You do it the same way you do any Matter bridge.
Open the ikea app. Follow the instructions there to use the Dirigera hub as a “Matter bridge.” This will generate a QR code.
Open the SmartThings app. Go to add a device, then choose Matter (not IKEA), then follow the instructions there to use the QR code you got from IKEA.
If this is the first time you have added a matter device to your account, see the FAQ on what you need:
FAQ: What do I need to add a Matter device to the SmartThings app? Do I need a bridge router device?
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And that’s it. The dirigera hub should be added as a matter bridge and it will bring over some of its attached devices. You will then be able to use those devices like any other device on your SmartThings account.
Note that the IKEA matter bridge feature is currently still in beta and likely to be for quite a while. It is not available yet to all IKEA customers, so if it doesn’t show up any IKEA app, you have to wait until it does.
And at the time of this posting it only supports lighting. No sensors, buttons, air purifiers, speakers, or anything else yet. Just the smart bulbs and items with built-in bulbs.
Because of that, there’s not much reason to use this method with SmartThings yet. Those same devices can already be added directly as individual Zigbee devices to a smartthings/aeotec hub. And that method already runs local. But you will get one benefit: because matter will allow you to use it with both the IKEA app and the SmartThings app at the same time, you will be able to use the IKEA app to perform firmware updates when needed. So that’s something.
As for how well it works, I’ve only seen a couple of reports on other forums of people who have tried connecting the dirigera hub to SmartThings via Matter. Most people said it went fine, a few were unable to make the connection, but they didn’t appear to understand the Wi-Fi issues required for initial set up, including IPv6 support, so they would’ve had the same problem with any matter over Wi-Fi device. (Again, see the community FAQ linked to above.) But those who already had matter working said it added fine.
So not much news yet. Note that if you already have IKEA Smart bulbs, you would have to remove them from SmartThings and connect them to the Dirigera hub before starting this whole process, so you would have to re-create any routines have been using those. Also, if your Zigbee network had been using IKEA bulbs as repeaters, you’re going to lose those when you remove them from your SmartThings hub. So that’s just something to keep in mind. 
The matter bridge approach doesn’t give you a Zigbee connection to both a dirigera hub and a SmartThings hub. Instead, you first set up the smart bulb with a Zigbee connection to the matter bridge (in this case, the Dirigera hub) and then you set up a matter connection via WiFi between the matter bridge and your SmartThings hub.