FeSe$_{1-x}$Te$_{x}$ superconductors manifest some intriguing electronic properties depending on the value of $x$. In FeSe single crystal, the nematic phase and Dirac band structure have been observed, while topological surface superconductivity with the Majorana bound state was found in the crystal of $x sim 0.55$. Therefore, the electronic properties of single crystals with $0 < x leq 0.5$ are crucial for probing the evolution of those intriguing properties as well as their relations. However, this study is still left blank due to the lack of single crystals because of phase separation. Here, we report the synthesis, magnetization, electronic transport properties, and hydrostatic pressure effect of FeSe$_{0.67}$Te$_{0.33}$ single crystals free of phase separation. A structural (nematic) transition is visible at $T_{s} = 39$ K, below which the resistivity exhibits a Fermi-liquid behavior. Analysis of upper critical fields suggests that spin-paramagnetic effect should be taken into account for both $H parallel c$ axis and $H parallel ab$ plane. A crossover from the low-$H$ quadratic to the high-$H$ quasi-linear behavior is observed in the magnetoresistance, signifying the possible existence of Dirac-cone state. Besides, the strong temperature dependence of Hall coefficient, violation of (modified) Kohlers rule, and two-band model analysis indicate the multiband effects in FeSe$_{0.67}$Te$_{0.33}$ single crystals. Hydrostatic pressure measurements reveal that $T_{s}$ is quickly suppressed with pressure while $T_{c}$ is monotonically increased up to 2.31 GPa, indicating the competition between nematicity and superconductivity. No signature of magnetic order that has been detected in FeSe$_{1-x}$S$_{x}$ is observed. Our findings fill up the blank of the knowledge on the basic properties of FeSe$_{1-x}$Te$_{x}$ system with low-Te concentrations.
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