Teniste came through the Spordiklubi 10 youth academy and played for the club's first team in the IV liiga.

[4][5] On 1 September 2011, Teniste joined Norwegian club Sogndal on loan until the end of the season, with the option to make the deal permanent.

[6] He made his debut in the Tippeligaen on 11 September, in a 0–0 home draw against Aalesund, coming on as a substitute for Ole Jørgen Halvorsen in injury time.

[9] Teniste scored his first goal for Sogndal on 26 November 2017, in a 5–2 home win over Vålerenga in the last match of the 2017 season.

Teniste made his senior international debut for Estonia on 9 November 2007, replacing Urmas Rooba in the 70th minute of a 0–2 away loss to Saudi Arabia in a friendly.