  In this paper, we carry out an investigation into the semileptonic decays
$D_s^+ \to K^0\ell^+\nu_\ell$ with $\ell=(e,\mu)$ by employing the QCD
light-cone sum rules approach. The vector transition form factor (TFF)
$f_+^{D_s^+ K^0}(q^2)$ for $D_s^+\to K^0$ decay is calculated while considering
its next-to-leading order contribution. Subsequently, we briefly introduce the
twist-2, 3 kaon distribution amplitudes, which are calculated by using QCD sum
rules within the framework of the background field theory. At the large recoil
point, the TFF has $f_+^{D_s^+ K^0}(0)=0.692_{-0.026}^{+0.027}$. Then, we
extrapolate $f_+^{D_s^+ K^0}(q^2)$ to the whole physical $q^2$-region via the
simplified $z(q^2,t)$-series expansion, and the behavior of TFF $f_+^{D_s^+
K^0}(q^2)$ is exhibited in the numerical results part, including the
theoretical and experimental predictions for comparison. In addition, we
compute the differential branching fraction $\mathcal{B}(D_s^+ \to
K^0\ell^+\nu_\ell)$ with the electron and muon channels, which are expected to
be $\mathcal{B}(D_s^+ \to K^0e^+\nu_e)=3.379_{-0.275}^{+0.301}\times 10^{-3}$
and $\mathcal{B}(D_s^+ \to K^0\mu^+\nu_\mu)=3.351_{-0.273}^{+0.299}\times
10^{-3}$ as well as contained other results for comparison. Our results show
good agreement with the BESIII measurements and theoretical predictions.
Furthermore, we present our prediction with respect to the CKM matrix element
$|V_{cd}|$ by using the $\mathcal{B}(D_s^+ \to K^0e^+\nu_e)$ result from BESIII
Collaboration, yielding $|V_{cd}|=0.221_{-0.010}^{+0.008}$. Finally, we provide
the ratio between $D_s^+ \to K^0e^+\nu_e$ and $D_s^+ \to \eta e^+\nu_e$
channels, i.e. $\mathcal{R}_{K^0/\eta}^e=0.144_{-0.020}^{+0.028}$.
