  We introduce \texttt{TEOBResumSP}: an efficient, accurate hybrid scheme for
generating gravitational waveforms from spin-precessing compact binaries. The
precessing waveforms are generated via the established technique of Euler
rotating the non-precessing \texttt{TEOBResumS} waveforms from a precessing
frame to an inertial frame. We obtain the Euler angles by solving the
post-Newtonian precession equations expanded to second post-Newtonian order.
Current version of \texttt{TEOBResumSP} produces precessing waveforms through
the inspiral phase up to the onset of the merger. We compare
\texttt{TEOBResumSP} to current state-of-the-art precessing approximants
\texttt{NRSur7dq4}, \texttt{SEOBNRv4PHM}, and \texttt{IMRPhenomPv3HM} for 200
cases of precessing compact binary inspirals with orbital inclinations up to 90
degrees, mass ratios up to four, and the effective precession parameter
$\chi_p$ up to 0.75. We further provide an extended comparison with
\texttt{SEOBNRv4PHM} involving 1030 more inspirals with $\chi_p\le 1$ and mass
ratios up to 10. We find that 91\% of the
\texttt{TEOBResumSP}-\texttt{NRSur7dq4} matches, 85\% of the
\texttt{TEOBResumSP}-\texttt{SEOBNRv4PHM} matches, and 77\% of the
\texttt{TEOBResumSP}-\texttt{IMRPhenomPv3HM} matches are greater than $0.965$.
Most disagreements occur for large mass ratios and $\chi_p \gtrsim 0.6$. We
identify the mismatch of the \emph{non}-precessing $(2,1)$ mode as one of the
leading causes of disagreements. We also introduce a new parameter,
$\chi_{\perp,\text{max}}$, to measure the strength of precession and hint that
the mismatch between the above approximants shows an exponential dependence on
$\chi_{\perp,\text{max}}$ though this requires further study. Our results
indicate that \texttt{TEOBResumSP} is on its way to becoming a robust
precessing approximant to be employed in the parameter estimation of
generic-spin compact binaries.
