  We use an effective field theory (EFT) approach to calculate the next to
leading order (NLO) gravitational spin-orbit interaction between two spinning
compact objects. The NLO spin-orbit interaction provides the most
computationally complex sector of the NLO spin effects, previously derived
within the EFT approach. In particular, it requires the inclusion of
non-stationary cubic self-gravitational interaction, as well as the
implementation of a spin supplementary condition (SSC) at higher orders. The
EFT calculation is carried out in terms of the non-relativistic gravitational
field parametrization, making the calculation more efficient with no need to
rely on automated computations, and illustrating the coupling hierarchy of the
different gravitational field components to the spin and mass sources. Finally,
we show explicitly how to relate the EFT derived spin results to the canonical
results obtained with the ADM Hamiltonian formalism. This is done using
non-canonical transformations, required due to the implementation of covariant
SSC, as well as canonical transformations at the level of the Hamiltonian, with
no need to resort to the equations of motion or the Dirac brackets.
