Kostek's first modeling job was for a series of television commercials for boutique Ciao Bella in 2013 which aired on MTV, E! News, VH1, and ABC Family. She then joined her first modeling agency in Boston in 2015, and subsequently became brand ambassador and model for Benrus, Equinox Fitness, and Dune Jewelry. Her early work consisted of print and television advertisements for brands like Nissan, New Balance, and Rebag to name a few. She also graced the covers of luxury lifestyle magazines like Ocean Drive, BELLA, and Haute Living among others.Since then, Kostek has done campaigns and ambassadorships for various clothing and cosmetic brands including L'Oréal, Victoria's Secret, and Clarins. She also did ad campaigns for fashion line Kittenish, and walked the runway for its Spring/Summer 2019 collection at New York Fashion Week. Kostek also models for Reebok, and headlined the brand's PureMove Bra and Amazon storefront campaigns among others. Kostek initially found difficulty securing modeling representation as agencies kept telling her she was not tall enough at 5'8", or thin enough at dress size 4/6. She eventually submitted a video of her experience to the Sports Illustrated Swimsuit Issue which was conducting an open casting call at the time. She was scouted, and walked the runway for the SI Swimsuit Fashion Show during Miami Beach Swim Week in July 2017. The following month, she was photographed by Yu Tsai in Belize for her first photoshoot with the magazine for the 2018 issue. Kostek was chosen from 5,000 open casting call candidates and won the inaugural Sports IllustratedSwim Search in March 2018. She walked the runway for Miami Beach Swim Week for the second time in July 2018, and closed the show the following year. The first model announced for the 2019 issue, she did her shoot in South Australia with photographer Josie Clough, and landed a solo cover in her official year as a rookie. Kostek has been called an "American Bombshell" and sex symbol for her blonde hair, blue eyes and curves. Connecticut Magazine named her in their "40 under 40" list of influential people of 2018, and she was included in Maxim's Hot 100 list of Sexiest Women in the World in 2019.
In 2018, Kostek released a jewelry line called the Voyager Collection in collaboration with Dune Jewelry. The following year, she and the company released her namesake collection which she designed. She has also released clothing and accessory inspired by her trademarked phrase, "Never Not Dancing". Kostek started touring universities and colleges in the U.S. in 2019 for her "Own It" Tour where she conducts talks on self-acceptance and body image.
Since 2018, Kostek has supported California Strong which helps families with tragedies in the state. Kostek and her partner donated more than 20,000 personal protective equipments to hospitals and fire departments during the COVID-19 pandemic. She has also read for Save With Stories benefiting Save the Children and No Kid Hungry foundations.
A classically trained dancer, Kostek often posts videos of herself on social media spontaneously dancing in places outside a dance studio. Her catchphrase, "Never Not Dancing," caught on and inspired others to do the same. Since 2015, Kostek has been in a relationship with American football player Rob Gronkowski.