Kashyap served in the Indian Air Force as an airman from 1988 to 2004.
He began as a member of the Block Development Committee, Pachhad (2005–2010), joined the BJP in 2006, and served as Sirmaur district president and later state general secretary of the BJP SC Morcha. He was elected MLA from Pachhad in 2012 and re-elected in 2017.
In 2019 he won the Shimla Lok Sabha seat. On 22 July 2020 he was appointed president of the Himachal Pradesh BJP, a post he held until 2023. In 2024 he retained Shimla, defeating Congress candidate Vinod Sultanpuri by 91,451 votes (5,19,748 to 4,28,297).
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