General Řehka was born in February 1975. He was educated at the Military Grammar School in Opava (1989–1993) and graduated from the Military University of Ground Forces in Vyškov in 1997 with a specialization in reconnaissance.

He was commissioned in 1997 and served in special reconnaissance and special operations units, later holding positions including senior foreign liaison officer and Chief of the JTAC Group. In 2003, he joined the 601st Special Forces Group, where he served in senior roles and later as commander (2010–2014). He subsequently served as Director of the Special Forces Directorate (2014–2017) and as a staff officer at HQ Allied Rapid Reaction Corps in Germany (2006–2009).

In 2017, he was appointed Deputy Commander of NATO Multinational Division Northeast in Poland, serving until 2020. He then led the National Cyber and Information Security Agency (2020–2022). Since 1 July 2022, he has served as Chief of the General Staff of the Czech Armed Forces.