<p>This study examines the linear instability of double-diffusive rotational convection in a horizontal layer of Navier–Stokes–Voigt fluid with stress-free boundary conditions. The onset condition for convection is derived in closed form using normal mode analysis. Double-diffusive convection in the presence of rotation serves as an example of a triple-diffusive fluid system, exhibiting convective behaviours not observed in double-diffusive Kelvin–Voigt fluid models. Numerical calculations reveal several novel and significant phenomena under specific parametric conditions: (i) the emergence of a closed and disconnected oscillatory neutral stability curve from its stationary counterpart, necessitating three Rayleigh numbers to characterise the onset of instability, unlike the classical single-parameter framework; (ii) the destabilisation of a double-diffusive Navier–Stokes–Voigt fluid layer under the influence of rotation and (iii) the destabilisation of rotating convection in a Navier–Stokes–Voigt fluid layer due to the addition of a stable solute concentration gradient. These findings highlight the complex interplay between rotation, solutal stratification and viscoelasticity, offering fresh insights with implications for industrial processes, geophysical flows and astrophysical environments. Validation against established benchmarks affirms the accuracy of the analysis and demonstrates how, even within the Navier–Stokes–Voigt framework, traditionally stabilising factors can collectively act as catalysts for convective instabilities under specific conditions.</p>