  We generalize to Kerr spacetime previous gravitational self-force results on
gyroscope precession along circular orbits in the Schwarzschild spacetime. In
particular we present high order post- Newtonian expansions for the gauge
invariant precession function along circular geodesics valid for arbitrary Kerr
spin parameter and show agreement between these results and those derived from
the full post-Newtonian conservative dynamics. Finally we present strong field
numerical data for a range of the Kerr spin parameter, showing agreement with
the GSF-PN results, and the expected lightring divergent behaviour. These
results provide useful testing benchmarks for self- force calculations in Kerr
spacetime, and provide an avenue for translating self-force data into the
spin-spin coupling in effective-one-body models.

General Relativity and Quantum Cosmology