How much do you want it to shine?
The highest gloss probably is a hard poly or varnish finish. The disadvantage of that (besides an assault on tradition) is a hard glossy finish shows every ding and scratch, and cannot be touched up.
Using wax on polished briar can also result in a high gloss, but one that is more forgiving of tiny dings and dents. It also does not last, and must be renewed often, but wax is cheap.
I try and keep an obsessive number of pipes shining.
I do have beeswax, and use it on my glossiest pipes.
But by far and away the easiest, quickest, and I think most attractive glow on briar is obtained from:
Using 4/0 grade steel wool, paper towels, and 190 proof Everclear to remove all little dings and dirt.
Then just as little grapeseed oil as I can apply using a paper towel.
A $10 12 ounce bottle of grapeseed oil will likely last a lifetime.
ORGANIC GRAPESEED OIL, COLD PRESSED. Ingredients: Grapeseed oil, 100% Pure with NO additives or carriers added. It is noted to be especially effective to help the skin around the eyes. It's commonly used in stretch mark preparations.
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A bag of 4/0 steel wool costs $6 and lasts me a year.
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Every pipe I show off here, gets a grapeseed oil glow. It’s not a shine.
If you want, you can shine it up with wax.