Only chance to win a medal in a new sport is basketball, but I think we'll just be happy to qualify first.
Fencing and tennis we haven't won medals since 1896, so medals in those sports will basically be new sports at this point
Also in water polo both our men and women have won Olympic medals, but no gold.
For a medal in a new event, I guess there are a lot of them. Men's team (basketball), women's sabre (fencing), women's 70 kg (judo), women's pair (rowing), women's double sculls (rowing), men's skeet (shooting), women's skeet (shooting), mixed skeet (shooting), women's singles (tennis), mixed doubles (tennis), women's 53 kg (wrestling), men's 74 kg freestyle (wrestling). 1988 was the last time we did not win a medal in a new event so I guess it's quite likely to win a medal in at least one of these.