  One of the main problems in Particle Physics is to understand the origin and
nature of Dark Matter. An exciting possibility is to consider that the Dark
Matter belongs to a new complex but hidden sector. In this paper, we assume the
existence of a strongly interacting dark sector consisting on a new scalar
doublet and new vector resonances, in concordance with a model recently
proposed by our group. Since in a previous work it was found that it is very
challenging to find the new vector resonances at the LHC, here we study the
possibility of finding them at the a future Compact Linear Collider (CLIC)
running at $\sqrt{s}=3$ TeV. We consider two distinct scenarios: when the
non-standard scalars are heavy, the dark resonance is intense enough to make
its discovery possible at CLIC when the resonance mass is in the range
$[2000,3000]$ GeV. In the second scenario, when the non-standard scalars are
light, the new vector boson is too broad to be recognized as a resonance and is
not detectable except when the mass of the scalars is close to (but smaller
than) a half of the resonance mass and the scale of the dark sector is high. In
all the positive cases, less than a tenth of the maximum integrated luminosity
is needed to reach the discovery level. Finally, we also comment about the
mono-$Z$ production.
