Prompt $\gamma$-ray production cross sections are important for nuclear reaction and structure calculations and in a number of applications. In particular, $\gamma$-ray production data and calculations are used in material assay and neutron diagnostics. ${}^{86}$Kr is a common, stable fission fragment, and as such can be used to test nuclear reaction models at the edge of stability, in order to improve calculations extending into unstable fission fragments in the region. Partial prompt $\gamma$-ray cross sections were measured, produced in neutron-induced reactions for neutron energies 11~MeV$< E_{n} <$80~MeV on ${}^{86}$Kr: three $\gamma$-rays of ${}^{85}$Kr and one $\gamma$-ray each in ${}^{82,83,84}$Kr and ${}^{83,85}$Br. A large part of the total cross section for the ${}^{86}$Kr$(n,3n{)}^{84}$Kr reaction is experimentally observed. The results are compared with predictions from calculations using the CoH${}_3$ reaction code and are used to check on the consistency of the parameters in the calculations.