In 2012, Eksteen was selected to represent the George-based at the premier South African rugby union competition for high schools, the Under-18 Craven Week, held in Port Elizabeth, scoring a try in their 33–39 defeat to Western Province. He joined the SWD Academy after leaving school and made four appearances for the s in the 2013 Under-19 Provincial Championship. He made just four appearances for them in the competition – three starts and one appearance off the bench – but was their top scorer in the competition with 76 points. That placed him as the third-highest points scorer in Group B of the competition. He scored six tries in his four appearances, which included a hat-trick in their match against the s, which saw him score 30 of his side's points in a 55–12 victory. The SWD U19 side qualified for the semi-finals of the competition, but Eksteen didn't feature in their 24–29 defeat to the in their semi-final match. He was included in the squad that participated in the 2014 Under-21 Provincial Championship. However, he just in just two matches against and – scoring 21 points through one try and eight conversions in the latter match – before being joining the ' senior squad for the 2014 Currie Cup First Division. He made his first class debut as the SWD Eagles' starting fly-half in a 19–24 defeat to the in Kempton Park. After also starting their 31–22 victory over the in George, he scored his first senior points in their next match, scoring a try shortly before half-time in a 24–35 defeat at home to the. He appeared as a replacement in their 42–27 victory over the in Welkom in their final match of the regular season, as well as in their 43–45 defeat to the same opposition in the semi-finals a week later. With the senior side's season over, he rejoined the Under-21 side that reached the final of Group B of the Under-21 Provincial Championship, starting the match and scoring his side's only points as the s won the match 46–3. Despite still being eligible to represent SWD at Under-21 level in 2015, he exclusively played for the senior side. He played off the bench in all eight of their 2015 Vodacom Cup matches. Eksteen scored one try in their defeat to as his side finished in fourth position on the Southern Section log to qualify for the quarter finals, where they lost to the. He appeared in all six of their matches during the 2015 Currie Cup qualification series – showing his versatility as he twice started as a scrum-half, twice started as a fullback and twice played off the bench – and again contributed a single try during the competition, in a 19–13 victory over the. However, that was his side's only victory in the competition as they finished bottom of the log and qualifying to play in the 2015 Currie Cup First Division competition. Eksteen was handed the kicking duties during this competition and it coincided with a big turnaround in fortunes, as the SWD Eagles won four out of their five matches, to finish in third spot on the log to qualify for the semi-finals. Eksteen contributed 102 points in these five matches to not only be the SWD Eagles' top scorer in the competition, but also the overall top scorer, ahead of champions ' Adriaan Engelbrecht. His best points haul during the competition came in a 47–40 victory over the in the semi-final, as he scored one try, two conversions and six penalties to contribute 27 points and help the SWD Eagles reach their first final since 2010. He kicked ten points in the final, but it was not enough, as the Leopards ran out 44–20 winners.
Southern Kings
At the start of 2016, Eksteen was one of two SWD Eagles players that joined the ' Super Rugby squad for a trial period as they prepared for the 2016 Super Rugby season.
