  We construct an efficient frequency domain waveform for generic circular
compact object binaries that include neutron stars. The orbital precession is
solved on the radiation reaction timescale (and then transformed to the
frequency domain), which is used to map the non-precessional waveform from the
source frame of the binary to the lab frame. The treatment of orbital
precession is different from that for precessional binary black holes, as
$\chi_{\rm eff}$ is no longer conserved due to the spin-induced quadrupole
moments of neutron stars. We show that the new waveform achieves $\le 10^{-4}$
mismatch compared with waveforms generated by numerically evolved precession
for neutron star-black hole systems for $\ge 90\%$ configurations with
component mass/spin magnitude assumed in the analysis and randomized initial
spin directions. We expect this waveform to be useful to test the nature of the
mass-gap objects similar to the one discovered in GW 190814 by measuring their
spin-induced quadrupole moments, as it is possible that these mass-gap objects
are rapidly spinning. It is also applicable for the tests of black hole
mimickers in precessional binary black hole events, if the black hole mimicker
candidates have nontrivial spin-induced quadrupole moments.
