You can get replacement after-market tabs like this https://www.dogearsgps.com or this https://www.merlincycles.com/raceware-garmin-tab-repair-part-104501.html I fitted the Raceware version to my Edge 1000 and it has staid stuck on for 6 months. The "click" into the mount is perhaps not as positive as the original Garmin mount, but it is fine. The replacement mount sits on top of the old mount, which you have to file down, so the Garmin sits a bit higher than it used to. This give me more clearance for a charging cable.
The other way is to find a replacement back on a well known auction site, and swap it over. The problem with this is that a secondhand back may well have worn tabs, as well as the problem of fitting it yourself.
The Garmin mount is integral to the back of the unit, and Garmin don't sell new replacement backs or offer a cost-effective replacement of just thus part. There is an option to send in your old Garmin and get a new / refurbished one in return for £200 (around 50% of the cost of a new one), or a 30% credit against a new 1030 in return for the old unit. This seemed an expensive way to get a worn plastic mount replaced, so I went with the DIY option. In an ideal world, the Garmin Edge would have a user-replaceable mount, so that this part of the device can be replaced when it inevitably wears out. Even my 15 year-old Garmin eTrex has a replacement mount that screws on the back, so you can replace just that part if it fails.
