Engstler began competitive karting in 2009 at nine years old and remained in karts until 2014. He moved into circuit racing via the ADAC Formula 4 series in 2015 and 2016, scoring two championship points across both seasons, before switching to touring car competition in 2017.
From 2017 onwards Engstler accumulated an extensive record across the global TCR landscape, competing in the ADAC TCR Germany, TCR International, TCR Middle East, TCR Asia, TCR Europe, TCR China, TCR Malaysia, and WTCR series. He took his first circuit podiums at Oschersleben in 2017 in the ADAC series, and was announced as a TCR International entry with the Junior Team Engstler squad that same June.
His most productive TCR years were 2018 and 2019. He won the TCR Asia Series in both seasons, the TCR Middle East championship in 2019, and the TCR Malaysia title in 2019 and 2020. In the TCR Europe series in 2019 with M1RA, he finished ninth overall and claimed a controversial win at the Red Bull Ring after making contact with Luca Filippi on the final lap.
Engstler entered the WTCR full-time in 2020 in a Hyundai i30 N TCR for the family team, finishing sixteenth in the championship with a best result of eighth. Returning for 2021, he scored his maiden WTCR podium at the Nordschleife and won the WTCR rookie championship by a single point over Gilles Magnus. That same year he clinched the ADAC TCR Germany title with two rounds to spare.
In 2022 Engstler moved into GT3 competition, joining Rutronik Racing for the ADAC GT Masters alongside Patric Niederhauser. The pair opened with a second place at Oschersleben and were consistently in the top ten, finishing fourteenth overall.
Engstler graduated to the DTM in 2023 with an Audi R8 LMS Evo II fielded by the family team, managing a best race finish of seventh and ending the year twenty-fourth in the standings. During the same season he raced at the 24 Hours of Spa with Scherer Sport PHX alongside Kelvin van der Linde and Nicki Thiim, finishing third overall.
For 2024, Engstler switched to Lamborghini customer team GRT within the DTM. At the opening Oschersleben round he qualified fourth for Sunday's race, but a well-timed full-course yellow elevated him to first on the road. He held off Maro Engel in the closing stages to secure his first DTM victory.
Engstler's championship haul in Asian and regional TCR series establishes him as one of the most well-travelled touring car drivers of his generation. His DTM win at Oschersleben, mirroring his father's milestone at the same circuit, gave his career an additional layer of family significance that underscored the Engstler name's place in international touring car racing.