  We study the star-forming (SF) population of galaxies within a sample of 209
IR-selected galaxy clusters at 0.3$\,\leq\,z\,\leq\,$1.1 in the ELAIS-N1 and
XMM-LSS fields, exploiting the first HSC-SSP data release. The large area and
depth of these data allows us to analyze the dependence of the SF fraction,
$f_{SF}$, on stellar mass and environment separately. Using $R/R_{200}$ to
trace environment, we observe a decrease in $f_{SF}$ from the field towards the
cluster core, which strongly depends on stellar mass and redshift. The data
show an accelerated growth of the quiescent population within the cluster
environment: the $f_{SF}$ vs. stellar mass relation of the cluster core
($R/R_{200}\,\leq\,$0.4) is always below that of the field
(4$\,\leq\,R/R_{200}\,<\,$6). Finally, we find that environmental and mass
quenching efficiencies depend on galaxy stellar mass and distance to the center
of the cluster, demonstrating that the two effects are not separable in the
cluster environment. We suggest that the increase of the mass quenching
efficiency in the cluster core may emerge from an initial population of
galaxies formed ``in situ.'' The dependence of the environmental quenching
efficiency on stellar mass favors models in which galaxies exhaust their
reservoir of gas through star formation and outflows, after new gas supply is
truncated when galaxies enter the cluster.
