Vectorlike quarks~(VLQs) with masses at the TeV-scale have been predicted in many new physics scenarios beyond the Standard Model~(SM). Based on a simplified $\left(X,T\right)$ doublet model including the exotic vectorlike $X$ quark~(VLQ-$X$) with electric charge $5/3$, we study the production of the VLQ-$X$ decaying into $tW$ at the future Compact Linear Collider~(CLIC) with $\sqrt{s}=3$ TeV including the initial state radiation and beamstrahlung effects. We focus on the final signals including same-sign dilepton~(electrons or muons), at least one $b$-tagged jet and large missing transverse momentum.
By performing a detailed signal-to-background analyses and detector simulations, we obtain the $2\sigma$ exclusion capabilities and the $5\sigma$ discovery reaches, respectively, on the mass of VLQ-$X$ $m_{X}$ and the relevant parameters~($Br(X\to tW)$ for $m_{X}<1500$~GeV and the coupling strength $g^{*}$ for $m_{X}\geq1500$~GeV) for some typical luminosities at 3 TeV CLIC.