We usually keep pizza dough in the fridge for three days before making the pizza. We use the normal ingredients such as flour, sugar, salt, yeast, olive oil and water. I think this specific one has garlic powder and dried herbs added. Due to circumstances, we might have to keep it longer than three days this time. Will it be okay to keep it for a week?
"Will it be okay" could mean a few different things. Are you concerned about safety? Flavor? Other dough characteristics?
In terms of food safety, it's not the best practice to do with dough that lacks preservatives (added or natural, like in sourdough), but a week under refrigeration is pretty unlikely to result in anything really bad happening to dough unless it was already contaminated with bad bacteria or something. If it's very moist and stored in a way that accumulates moisture on the surface, I suppose it's possible to start growing some mold, but even that's pretty unlikely to be significant within a week. If you want to be extra cautious, be sure to cook the dough thoroughly (though generally with pizza you're unlikely to end up with raw dough in the center anyway).
Regarding flavor, here's where growth may cause problems. Excess yeast growth may result in a flavor that's overly yeasty or alcoholic in tone, perhaps a bit "off." More likely, you will probably get some lactic acid bacteria growth starting, resulting in a slight "sourdough" kind of flavor. However, mature sourdough cultures are meant to be relatively stable, where the lactic acid bacteria will easily outcompete other microorganisms in the dough and sour it enough to prevent other things from growing. Your dough (presumably made with commercial yeast) hasn't stabilized into a cycle like sourdough, so it's also possible that other things will grow during the week, potentially leading to various "off" or "funky" smells or flavors in the dough. Again, I think the most likely outcome is a "sourdough" flavor that will probably be somewhat good, but it's a bit unpredictable when you store dough this long.
Finally, you might be concerned about how the dough will behave. Generally, about three days is the maximum for most typical dough mixes before yeast start to use up their food and other microorganisms might start to interfere with further yeast growth. There's usually a gradual decline starting after day three or so: by seven days, you may get significantly less yeast growth if you take it out of the fridge and expect the dough to proof before baking. (I don't know what your procedure is. With my pizza dough, I typically degas and shape thoroughly after removing from the fridge, then let my dough sit for a few hours at room temperature to grow more bubbles before baking. You may not be able to get much rise out of this dough after so long, so you might consider how you want to handle it.) On the other hand, it really depends on how much yeast was in the original mix and what starts growing over the week. A thorough degassing and redistribution of the yeast could actually reinvigorate the dough and allow it to proof fine even after several days.
If the dough is not tightly sealed or has some areas more exposed to air, they may dry out after so long. This can lead to tough spots in the dough. Perhaps of a greater concern is the effect of acid, alcohol, and other waste products in a dough this old. While unlikely to cause a lot of problems after a week in the fridge, my experience with overproofed doughs at room temperature and overproofed sourdoughs is that eventually you'll start to see breakdown in the gluten structure, which can cause the dough to tear much more easily or not stretch evenly when making pizza. (I once had an overproofed sourdough pizza dough that literally tore apart into about three or four pieces as I was trying to load it into the oven; all the acid made it much more fragile.) Again, this is probably not a huge concern for normal pizza dough with commercial yeast, but be prepared for the dough to behave more erratically when stretching and preparing for bake. Seven days of fermentation will also change various chemical characteristics of the dough (like sugar content, enzyme breakdown of some elements, etc.), so be prepared for the baking to be a little different. In particular, browning may happen at a different rate than you normally expect.
In general, it will probably be fine, though it might have somewhat different flavor notes and will rise less. However, it's a bit unpredictable, which is why most people don't retard dough for more than around three days. If this situation recurs, I'd strongly recommend simply freezing the dough: pizza dough can be frozen for at least a couple months with few concerns about quality. A few hours to defrost and you're likely to have a much more predictable experience.