Nope. No ideas. All I can suggest is you find someone who can make a new grate that would sit more flush. You can't cover it or it won't do its job.

Assuming it is indeed the fresh air intake, and not the old vent for a basement furnace? We lived in an old house once that had ALL the heat for the entire house come gushing up through a similar floor vent in the center of the house. If that is the case, it can be covered. But not if it is the fresh air intake.

In a rental, there isn't much you can do. Find out what type of vent it is before going much further (air pulling INTO the vent vs. air pushing OUT of the vent).

It is a fresh air intake and cannot be covered fully. I was thinking of taking a larger rug, cutting out the size if the vent then laying that over the cover to keep the edges from potentially hurting me.

Creative idea with cutting out a rug. Another possible solution is to nail down thin wood threshold trim. It won't be flush but it won't be sharp either.

Tell landlord it's a hazard. It's his issue. But if you want some control do your research. You can buy grates online but if it is an odd size custom made- you can find iron work craft people.

Your going to need a custom made flush mount vent. I agree it is going to be many hrs of labour to frame/block it in and install.

one thing your landlord could do is buy the closest size flush grate and frame it in. the work is the same but the grate is cheaper.

You are stuck with the grate - however you can possibly make it not a trip hazard by installing screws that fasten it to the floor. They would need to be done so the screws sit as flush as possible.

May I have your permission to use these two pictures of the vent in the hallway on my website for a story I wrote?