You might be able to replace the broken slats, or find a repairer to do it for you. (I'd not be surprised though if the latter didn't make economic sense).
But....
Are the slats plastic? If so they may have been embrittled by UV radiation, and the old ones all become prone to breaking.
No chance of a butt joint working, and layering something over the joint would look pants and could well stop the slats nestling together when the blind is up or rotating when it's down.
Seek out a blind expert for confirmation, but I'm sure it's new slats or new blind time...
Want to reply to this thread or ask your own question?
You'll need to choose a username for the site, which only take a couple of moments. After that, you can post your question and our members will help you out.