It's possible to mix yeast and mother for a new batch but if that mother has a significant amount of acetic acid as liquid, I'd imagine it could stunt fermentation. I know a lot of people also keep their vinegar in a solera so they remove a gallon of finished usable vinegar and then replace it with wine or cider to keep it rolling.
Though there was a period when shrub was a common drink - and shrub is a drinkable vinegar. A basic recipe for shrub is 1 lb of fruit of your choice (in season would be preferable ) 1 C water , 1 C vinegar and 1 C sugar. You almost boil the fruit with the vinegar (heat to about 190 F) and add the sugar then the water and this makes a drinkable vinegar that was all the rage in the 19th and early 20th C.