Concerns about sustainability in apparel has shifted from fast-fashion makers like H&M and sportswear giants like Nike to the luxury industry, with its reliance on animal-based materials like leather and cashmere. Prada SpA pledged last month to transition to recycled nylon for its iconic belt bags and backpacks, while Kering chief Francois-Henri Pinault —whose company owns Gucci and Saint Laurent—is spearheading an effort to get fashion makers to commit to new sustainability targets.