  Besides the exactly solvable spin-1/2 Kitaev model, higher spin-$S$ ones, not
exactly solvable, are promising playgrounds for researches on the quantum spin
liquid as well. One of the main interests in higher spin-S cases is the
interplay between the Kitaev spin liquid (KSL) and spin nematics. We probe this
interplay in a spin-1 model on the honeycomb lattice with competing
bilinear-biquadratic and Kitaev interactions. Utilizing the 2D infinite
projected entangled-pair state (iPEPS), we map out the phase diagram for the
ferro-biquadratic interaction. In the phase diagram, we discover the direct
KSL--spin-nematics transitions in the vicinity of pure Kitaev limits. It has
been revealed that the ferro KSL exhibits robustness against perturbations from
ferro-quadrupolar interactions. Also, the spin-nematic phase is extended to the
parameter region near the antiferro-Kitaev limit.
