  We perform the first investigation of the process $e^{+}e^{-}\to
K^+K^-\psi(2S)$ and report its Born cross sections over a range of
center-of-mass energies from 4.699 to 4.951~GeV. The measurements are carried
out using several partial reconstruction techniques using data samples
collected by the BESIII detector with a total integrated luminosity of
2.5~fb$^{-1}$. We search for new tetraquark candidates $Z_{cs}^\pm$ in the
decays $Z_{cs}^\pm\to K^\pm\psi(2S)$. No significant $Z_{cs}^\pm$ signals are
observed.
