Since January 2021, he has been a non-executive director of BP plc; since October 2021, a senior advisor at Kohlberg Kravis Roberts; and since 2022, chairman of Swiss energy group Alpiq Holding.

[4] Teyssen's first career role was as a law clerk at the State Superior Court in Celle, Germany.

In January 2012, he spoke out against the European Union Emission Trading Scheme (EU ETS) and in 2013, he questioned the profitability of gas-fired plants.

[8][9] In August 2010, Teyssen and around 40 other prominent figures signed the Energy Policy Appeal for an extension of the operating lives of German nuclear power plants.

[16] Teyssen was Norwegian Honorary Consul General until the end of 2020, responsible for the German states of North Rhine-Westphalia, Rhineland-Palatinate and Saarland.

[25] His father, Hans Teyssen, was Vice President of the Higher Regional Court of Celle for many years and most recently Ministerial Director in the Lower Saxony Ministry of Justice; his uncle, Anton Teyssen, was a member of the Christian Demokratic Union of the state parliament for Hildesheim for many years.