Kilp first appeared internationally in February 2011 at the European Youth Olympic Winter Festival 2011 in Liberec . There he finished 51st place over 7.5 km freestyle, 34th place over 10 km classic and 11th place in sprint. In the Scandinavian Cup he started for the first time in December 2011 in Vuokatti and achieved 120th place in the 3.75 km freestyle. In January 2012 he made his debut in Otepää in the cross-country skiing world cup . He came in 57th place in the sprint. At the Nordic World Ski Championships 2015 in Falun , he reached 36th place in the sprint. At the beginning of the 2016/17 season he got his first World Cup points in Ruka with 13th place in the sprint. At the Nordic World Ski Championships in Lahti in 2017 , he finished 50th in the sprint and 14th place together with Raido Ränkel in the team sprint. In February 2018 he ran at the Olympic Winter Games in Pyeongchang to 18th place in the sprint and 17th place together with Karel Tammjärv in the team sprint. At the beginning of February 2019 he became the Estonian sprint champion in Otepää. At the Nordic World Ski Championships in 2019 in Seefeld in Tirol , he achieved 50th place in the sprint and, together with Raido Ränkel, 12th place in the team sprint.