  Galaxy clusters have long been theorised to quench the star-formation of
their members. This study uses integral-field unit observations from the
$K$-band Multi-Object Spectrograph (KMOS) - Cluster Lensing And Supernova
survey with Hubble (CLASH) survey (K-CLASH) to search for evidence of quenching
in massive galaxy clusters at redshifts $0.3<z<0.6$. We first construct
mass-matched samples of exclusively star-forming cluster and field galaxies,
then investigate the spatial extent of their H$\alpha$ emission and study their
interstellar medium conditions using emission line ratios. The average ratio of
H$\alpha$ half-light radius to optical half-light radius
($r_{\rm{e},\rm{H}\alpha}/r_{\rm{e},R_c}$) for all galaxies is $1.14\pm0.06$,
showing that star formation is taking place throughout stellar discs at these
redshifts. However, on average, cluster galaxies have a smaller
$r_{\rm{e},\rm{H}\alpha}/r_{\rm{e},R_c}$ ratio than field galaxies: $\langle
r_{\rm{e},\rm{H}\alpha}/r_{\rm{e},R_c}\rangle = 0.96\pm0.09$ compared to
$1.22\pm0.08$ (smaller at a 98\% credibility level). These values are
uncorrected for the wavelength difference between H$\alpha$ emission and
$R_c$-band stellar light, but implementing such a correction only reinforces
our results. We also show that whilst the cluster and field samples follow
indistinguishable mass-metallicity (MZ) relations, the residuals around the MZ
relation of cluster members correlate with cluster-centric distance; galaxies
residing closer to the cluster centre tend to have enhanced metallicities
(significant at the 2.6$\sigma$ level). Finally, in contrast to previous
studies, we find no significant differences in electron number density between
the cluster and field galaxies. We use simple chemical evolution models to
conclude that the effects of disc strangulation and ram-pressure stripping can
quantitatively explain our observations.
