We improve the non-relativistic QCD (NRQCD) action by comparing the dispersion relation to that of the continuum through $O(p6)$ in perturbation theory. The one-loop matching coefficients of the $O(p4)$ kinetic operators are determined, as well as the scale at which to evaluate $\alpha s$ in the $V$-scheme for each quantity. We utilise automated lattice perturbation theory using twisted boundary conditions as an infrared regulator. The one-loop radiative corrections to the mass renormalisation, zero-point energy and overall energy-shift of an NRQCD $b$-quark are also found. We also explore how a Fat$3$-smeared NRQCD action and changes of the stability parameter $n$ affect the coefficients. Finally, we use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation, to test how the improvements affect the non-perturbatively determined ${\rm Y}(1S)$ and $\eta b(1S)$ kinetic masses, and the tuning of the $b$ quark mass.