Heat/AC Unit Cover

It's called a "fan-coil unit" and it seems to be missing a front panel as its majority cause of ugliness.

Start with your building superintendent or maintenance person/department.

[Fan Coil Unit: a unit with a coil through which heated or chilled water is passed depending on the season, and a fan to blow air across that coil to heat or cool the apartment.]

Looks like you missing the front access panel. It's probably quite loud without it. Just make one from thin plywood and attach with some velcro or sheet metal screws.

These are called “package units” everything in 1 box. Quite popular in hotel/ motel and studio apartments. Yes there should be a cover in the front all the ones I have worked on have been metal, if you are renting I would ask the superintendent for a cover, with how strict some have said New York electrical laws are I would this to be a violation especially in a rental.

PTAC may be the official name but through the wall self contained unit. I can’t tell if the intake is at the bottom or the cover had it that’s the normal location ~12” tall most of the front bottom.