The term "Gestapo" is a contraction of "**Ge**heime **Sta**ats**po**lizei", and the last word "Polizei", which is feminine in German, determines the grammatical gender.

Cf also the very beginning of the [Spanish Wikipedia entry for Gestapo](https://es.wikipedia.org/wiki/Gestapo):

> La **Gestapo** (contracción de ***Ge**heime **Sta**ats**po**lizei*: 'Policía Secreta del Estado') fue la policía secreta oficial de la Alemania nazi (...)


Until the year 1936 the term "Gestapa" was also in use, a contraction of "**Ge**heimes **Sta**ats**p**olizei**a**mt", the last word being neuter in German.