In 1991/1992, Hintze briefly served as Parliamentary State Secretary at the Federal Ministry of Family Affairs, Senior Citizens, Women and Youth under minister Angela Merkel in the fourth cabinet of Chancellor Helmut Kohl.

From 2005 to 2013, Hintze served as Parliamentary State Secretary at the Federal Ministry for Economic Affairs and Technology under ministers Michael Glos (2005–2009); Karl-Theodor zu Guttenberg (2009); Rainer Brüderle (2009–2011); and Philipp Rösler (2011–2013) in the first and second cabinets of Chancellor Angela Merkel.

[citation needed] In the negotiations to form a coalition government of the Christian Democrats (CDU together with the Bavarian CSU) and the Free Democratic Party (FDP) following the 2009 federal elections, Hintze was part of the CDU/CSU delegation in the working group on foreign affairs, defense and development policy, led by Franz Josef Jung (CSU) and Werner Hoyer (FDP).

Later, in the negotiations to form a Grand Coalition of Merkel's Christian Democrats and the SPD following the 2013 German elections, he was part of the CDU/CSU delegation in the working group on bank regulation and the Eurozone, led by Herbert Reul and Martin Schulz.

[citation needed] In his capacity as vice-president, he was a member of the parliament’s Council of Elders, which – among other duties – determines daily legislative agenda items and assigning committee chairpersons based on party representation.