Stander's career began in his native South Africa, where he played between 2010 and 2012. He moved to Munster Rugby in 2012 and, after qualifying via residency in 2015, made his international debut for Ireland in 2016, before going on to earn 51 caps for his adopted country, as well as one cap for the British and Irish Lions in 2017.
In May 2017, the Mayor of Limerick, Kieran O'Hanlon, made Stander the city's inaugural honorary international ambassador. He was also named an honorary Limerick man at the Limerick Person of the Year awards in April 2021
Shortly after winning his 50th cap for Ireland, Stander announced that he would be retiring from rugby at the end of the 2020–21 season, citing a desire to raise his young daughter around his family in South Africa.
His 51st and final cap for Ireland was their 32–18 win against England in the final round of the 2021 Six Nations on 20 March 2021. In his final Six Nations campaign, Stander was named in the Team of the Championship.
After retiring, Stander and his family returned to South Africa and settled in the town of Paarl in the Western Cape. Having worked as a project manager in construction for a short period, Stander and his wife Jean-Marie have recently opened a boutique guesthouse in Franschhoek which is situated in the picturesque Cape Winelands of South Africa.