You can't really tell but the left nozzel is full of water.

I recommend replacing.

You need to get a plumber in to replace the shut off valve

There's no reason to delay the inevitable. Replace both valves, since they're the same age, while you have the area so accessible. Make sure they're all brass, inside and out. I like 1/4-turn ball valves.

Since shutting the water off is so inconvenient, I'd replace all of the old ones and be done with it.

Since I don't see a bucket under it, it can't be leaking that much.

I think that kind of shut off uses a washer. Over time, they harden and don't seal as well. Since you can't turn off the water to the whole unit (have you looked to see if there might be a main shut off in the utility closet?), you might as well get a plumber to replace all as suggested above.

Replacement valves are inexpensive, don't waste an opportunity to replace them while they're easily accessible.

Potential flooding of condo and neighboring units vs. inconveniencing the neighbors for a few hours. I know which ones your neighbors will wish you chose!

I live in a condo which has 122 units and ONE shut off valve for the building's water supply. In other words, if water to a unit has to be shut off for any reason, the whole building has water shut off.

In my experience, you can't replace a shut off valve without turning off the water for the building. You use the shut off valve so that you don't have to turn off water for the whole building to change a faucet or even a toilet.

I would double check with management or whoever is in charge of maintenance because based on personal experience, you would need to close down all the water to replace the shut off valves.

Because of the horrible consequences if a shut off valve breaks, my building has an annual inspection of all the shut off valves in each unit. If your shut off valve is found to be leaking or in danger of seizing (e.g. not shutting or opening properly), our building will make note of it. The HOA then turns off the water for one day so all homeowners on the list can get them replaced and the HOA generally provides the ability to use a plumber who bids a discount price. But the chief incentive is that normally it costs $2000 to shut off the water but there is no cost if you have the valves replaces on that day.

When I remodeled my kitchen, I replaced the old, wimpy shutoff valves for the kitchen sink with ball valves, as suggested by a couple of people above. I used compression fittings, so they were quick and easy to install (I didn't use a plumber). I never again have to worry about leaking, or failure to seal completely if I need to turn off water to the sink.

Eventually I'll replace every shutoff valve in the house.

They are easy to DIY, but a building's HOA may require a licensed plumber to perform the work as a way to protect the other tenants.

I was a little nervous about my first one and found this video to be the best, as far as instructions for the materials used in my house. When I was renovating, I had to replace several that were failing, and had the plumbers replace the others when they finally got around to my job. This gal has videos about other materials, as well.

BTW: this kind of valve is not likely to explode on you unless you try to take it apart. More likely is that the washer and/or seat with wear and leak when you try to turn it off.