Elle Mambetov grew up like any other young girl, playing with dolls whose outfits she wished matched hers and contemplating a fashion career after creating outfits with a sewing kit she received from her grandmother.

But what sets her apart is not her rise as a must-watch designer of modest fashion, but that her dreams are coming true through an innovative collection that’s part of Vogue magazine and the Council of Fashion Design of America’s A Common Thread fundraising initiative.

Mambetov, whose brand is Elle B Zhou, recently held a virtual show focused on modest fashion for fellow Muslim women...