I’m trying to find a short story by Asimov that I read years ago. The plot is that in the future, all meat is banned/illegal and carries a huge penalty if eaten/found. A few people can afford to buy it and eat it in places like opium dens. It’s treated like heroin is today.
I'll suggest "The Contraband Cow" by L. Sprague de Camp, first published in Astounding in 1942. Although it is not actually by Asimov as specified in the question, Sprague de Camp was a contemporary and a friend of his, which could lead to their work being confused.
It is set in a future USA, forming part of the "Federation of Democratic and Libertarian States". A Hindu majority in the Federation has forced through a law banning the consumption of "all animals of the subfamily Bovinae of the family Bovidae, the same comprising kine, buffaloes, bison, zebus, gayals, bantengs, yaks, and species closely related thereto", which mainly affects Americans wanting to eat steaks or roast beef. As far as I can see the penalties for being caught are not given, but I suppose they are reasonably grave.
Beef is available illegally from "steakeasies", and is produced either by local steakleggers (who are no problem to anyone), or on a larger scale by Mexican cartels. The parallels to illegal alcohol under Prohibition are very clear. Two researchers who are developing synthetic meat go to a secluded area to eat a steak, but one of them is first arrested by a Sikh Federal agent, and then kidnapped by a Mexican cartel who wish to shut down this competition to their trade. Various twist and turns of plot then
lead to the father of the Federal patrolman, an eminent Indian politician, overturning the anti-vacacide law, thereby assuring ruin for the cartels.