Cocondensation and postfunctionalization methods were employed to synthesize a mesoporous silica with large surface area (795.1 $\pm $ 1.1 m$^{2}$ g$^{-1})$ modified with 4-amino-5-hydrazino-1,2,4-triazole-3-thiol, which was successfully applied to adsorb and preconcentrate Cu(II), Co(II), and Cd(II) from aqueous media. Infrared spectroscopy of the adsorbent material demonstrated N-H stretching bonds related to primary amines existing in the ligand molecule, elemental analysis revealed the presence of 0.132 mmol g$^{-1}$ of nitrogen, scanning electron microscopy indicated globularly shaped particles with average size of 10 $\mu $m, and the point of zero charge was found to be 7.2. Kinetic data were applied to the pseudo-second-order model, indicating that a chemisorption mechanism is probably involved in the uptake of metal ions from aqueous solutions. According to the Langmuir model, the adsorption capacities for the different ions obey the following order: Cu(II) $>$ Co(II) $>$ Cd(II). Through a preconcentration system, a preconcentration factor of 18-, 15-, and 20-fold was attained for Cu(II), Cd(II), and Co(II), respectively. The proposed method was applied in the determination of trace metals in natural river water (Tiet\^{e} River) and the results were validated through standard reference material analysis. The results also indicated that the packed column proved to be stable over 24 adsorption/desorption cycles, demonstrating that the developed material is potentially suitable for the determination of trace-level metal ions in aqueous samples.