We performed $^{185/187}$Re nuclear quadrupole resonance (NQR) measurements under pressure to investigate the superconducting properties of noncentrosymmetric superconductor Cd$_{2}$Re$_{2}$O$_{7}$ under various crystal structures. The pressure dependence of superconducting transition temperature $T_{rm c}$ determined through ac susceptibility measurements is consistent with the results of previous resistivity measurements [T. C. Kobayashi $et al$., J. Phys. Soc. Jpn. 80, 023715 (2011).]. Below 2.2 GPa, in the nuclear spin-lattice relaxation rate $1/T_{1}$, a clear coherence peak was observed just below $T_{rm c}$, indicating conventional $s$-wave superconductivity. In contrast, the coherence peak disappears at 3.1 GPa, suggesting a change in superconducting symmetry to the $p$-wave dominant state against pressure.
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