Can I make this bookshelf safe without drilling into the wall?

If it wobbles now and is designed to be anchored, I wouldn’t load it with books and hope adhesive hooks will hold it. Books add up to a lot of weight, and those hooks aren’t a reliable substitute for an anti-tip attachment.

Check with the landlord about whether a proper anchor is allowed, especially if there may be a concern about what’s inside the wall. If not, a freestanding bookcase designed to stand on its own is the safer, simpler fix.

You could look into a floor-to-ceiling tension frame, then attach the shelf to that rather than the wall. But check the frame’s load rating and installation requirements, and make sure the floor and ceiling can take the pressure. It still needs to be firmly connected to the shelf, not just pressed nearby.

If the ceiling height or surface makes that a bad fit, I’d skip the workaround. A tension setup that shifts under load could make the whole thing less safe.

For a quick reality check, empty the shelf and see whether it stands steadily on its own, with the feet level and all the joints tight. A wider, properly fastened base might help with stability, but it won’t make a top-heavy or poorly assembled unit safe by itself.

Keep heavy items low, and don’t use it if it still rocks or tips with a gentle push. Given the wall gap and the missing backing, replacing it with a freestanding model may be less hassle than trying to convert it.