Telfer was born in Carluke and grew up supporting Rangers. He joined the club as a youth player after being spotted at a Football in the Community course at Bell College, Hamilton, when he was eight.
Playing career
Club
Rangers
After progressing through the Rangers academy, Telfer signed his first professional contract with the club in November 2011. He would make one competitive first team appearance for the club against Stenhousemuir in April 2014. On 13 May 2014, he was in the Rangers side that won the Scottish Youth Cup beating Hearts 8–7 on penalties following a 2–2 draw, at St Mirren Park. Telfer later describe playing in the Scottish Youth Cup Final as his biggest game of his life. At the end of the 2013–14 season, Telfer's future at Rangers appeared to be in doubt when Dundee United were reported to be keen to sign him. Dundee United then made a £50,000 bid to sign Telfer, which was rejected by Rangers, who offered him a new contract.
Dundee United
After rejecting the offer of a new contract with Rangers, Telfer signed for Dundee United in June 2014, with a compensation payment still to be agreed between the clubs. Telfer's departure from Rangers was commented on by the club's manager Ally McCoist, who described him as a "great prospect" and said that the club had wanted to keep him but it had been Telfer's decision to leave. The level of compensation to be paid was set by an independent tribunal, with Dundee United paying £200,000 to Rangers in January 2015. He made his Dundee United debut as a substitute against Aberdeen in the opening match of the 2014–15 season, and scored his first goal for the club in a 3–0 win over St Mirren on 1 November 2014. Telfer was named as SPFL Young Player of the Month for November 2014. On 1 January 2015 he scored United's sixth goal in a 6–2 Derby victory over local rivals Dundee. This was followed by two goals against Motherwell later that month. Telfer was a substitute for the Scottish League Cup Final, but was unused as Dundee United lost 2–0 to Celtic. He made 25 appearances and scored 4 times in his first season at the club. Having been unable to gain a regular place in the Dundee United team, Telfer moved on loan to Scottish Championship side Livingston in January 2016 until the end of the 2015–16 season. Telfer was released by United on 5 June 2017.
Almere City
Telfer signed for Dutch club Almere City in August 2017 on a one-year contract. He had been training with Dumbarton and Bolton Wanderers; rejecting a contract at the Macron Stadium to move to the Netherlands.
Greenock Morton
Telfer signed a one-year deal with Scottish Championship side Greenock Morton in June 2018.
Falkirk
On 18 June 2019, Telfer signed for Falkirk on a two-year contract.
International
Telfer has represented Scotland at under-17, under-19 and under-21 level.
