  We present the stellar mass ($M_{*}$), and K-corrected $K$-band absolute
magnitude ($M_{K}$) Tully-Fisher relations (TFRs) for sub-samples of the 584
galaxies spatially resolved in H$\alpha$ emission by the KMOS Redshift One
Spectroscopic Survey (KROSS). We model the velocity field of each of the KROSS
galaxies and extract a rotation velocity, $V_{80}$ at a radius equal to the
major axis of an ellipse containing 80% of the total integrated H$\alpha$ flux.
The large sample size of KROSS allowed us to select 210 galaxies with well
measured rotation speeds. We extract from this sample a further 56 galaxies
that are rotationally supported, using the stringent criterion $V_{80}/\sigma >
3$, where $\sigma$ is the flux weighted average velocity dispersion. We find
the $M_{K}$ and $M_{*}$ TFRs for this sub-sample to be $M_{K} / \rm{mag}= (-7.3
\pm 0.9) \times [(\log(V_{80}/\rm{km\ s^{-1}})-2.25]- 23.4 \pm 0.2$ , and
$\log(M_{*} / M_{\odot})= (4.7 \pm 0.4) \times [(\log(V_{80}/\rm{km\ s^{-1}}) -
2.25] + 10.0 \pm 0.3$, respectively. We find an evolution of the $M_{*}$ TFR
zero-point of $-0.41 \pm 0.08$ dex over the last $\sim $8 billion years.
However, we measure no evolution in the $M_{K}$ TFR zero-point over the same
period. We conclude that rotationally supported galaxies of a given dynamical
mass had less stellar mass at $z \sim 1$ than the present day, yet emitted the
same amounts of $K$-band light. The ability of KROSS to differentiate, using
integral field spectroscopy with KMOS, between those galaxies that are
rotationally supported and those that are not explains why our findings are at
odds with previous studies without the same capabilities.
