Yes! Sort of. I do this a lot. Advice:
As time goes by, the old brine will lose probiotics, as bacteria need food (sugars, etc) to stay alive. I’m not a scientist, but this is basically how it works.
So, if it’s been in the fridge for a couple of weeks, go for it. Months? I would probably start over, or just use “some“ of it.
Also, fermentation is a multistage life cycle sort of thing. So, almost anyone would tell you to use a mix of old brine and new. The old can jump start fermentation. The new ensures you get back to earlier, less acidic stages. This is particularly notable if your old brine is from a batch fermenting for a long time (months vs weeks).
Refrigeration pauses the fermentation process, so thats also worth thinking through. I’m not sure how long the ferment went, how long it’s been refrigerate, etc.
Alternative to consider… I have learned that my recipes come out best when I don’t create a water brine, but rather “dry salt“ a chili mash and let the peppers (or cabbage) give their own water to the recipe. You can’t dry salt everything. For example, I don’t think it would work with pickles
I can share some resources if interested.
Lastly, make sure it’s mold free, remove any yeast, and strain it.