Jelgrun was a member of the Bijani House of Representatives from 1981 until 2013, representing Kijuri County. He served as a Minister in the 3rd Ornam Government from 1985 to 1988. In the late 1980s, Jelgrun was an early proponent of a merger between the Liberal Democratic Party (LDP), of which he was a member, and the Bijani National Party (BNP). This put him at odds with Ornam's successor as Chief Minister, Ĉeso Dukan and Markom Hikoro, and he was not appointed to a ministerial position in either's government. Jelgrun was re-appointed to the Government in 1992, under Chief Minister Renar Mavasi, and was instrumental in merging the LDP and the BNP into the new Liberal National Party later that year.