Well, you can dry age a brisket or really any cut of beef at home, even a few days can make a difference. I typically don’t bother with it because it does take some space and a little setup.
Essentially, you’ll get a piece of meat that has less water content, (as the cut ages it will lose water) so the flavor of the beef itself will be more concentrated. Because of this, you may want to wrap it sooner in the cooking process and maybe even introduce some fat to it when you wrap it, you could use rendered beef fat, or butter (you can buy beef tallow and spread it like butter on the brisket) or whatever. You will of course wind up with a smaller cut to work with at the outset when the aging is done. Even a few days will make a difference, I wouldn’t go into aging for weeks and weeks at home without an entire really proper setup.
For a few days of dry aging, you can make a box out of a plastic tote. Perforate the hell out of it and the lid with a power drill, (except the bottom you don’t want beef juice dripping in your fridge) but you do want a good amount of airflow. Put the piece of meat onto a wire rack or something similar that fits into the storage box so you can get airlflow underneath and put some paper towels under it to catch any drippings. Pat the beef dry with paper towels before you put it into the box. - Also flip it once a day.
I personally would rub the outside of it with a little salt before placing it in the box, just a little, that will inhibit growth of anything crazy and start to build flavor and draw out moisture, If you do this step, Just remember you’ve already salted it a bit when you go to season it before the cook.
If you’re really curious you can weigh the brisket before you age it and after to get an idea of how much water has been drawn out.
A few days in a box like that will mimic the dry aging process and give you a deeper beef flavor in your cut of beef. The trade off though, is that if you get a “skin” from the drying process, the smoke won’t stick to the brisket as well as it normally would, you can remedy that a little by using mustard to stick your rub to the brisket, the tackiness will help the smoke stick to it as well.
This works for a prime rib roast too.