  We study the $f^+$ form factor for the semileptonic $\bar B_s\to
K^+\ell^-\bar\nu_\ell$ decay in a constituent quark model. The valence quark
estimate is supplemented with the contribution from the $\bar B^*$ pole that
dominates the high $q^2$ region. We use a multiply-subtracted Omn\`es
dispersion relation to extend the quark model predictions from its region of
applicability near $q^2_{\rm max}=(M_{B_s}-M_K)^2\sim 23.75$ GeV$^2$ to all
$q^2$ values accessible in the physical decay. To better constrain the
dependence of $f^+$ on $q^2$, we fit the subtraction constants to a combined
input from previous light cone sum rule [Phys. Rev. D 78 (2008) 054015] and the
present quark model results. From this analysis, we obtain $\Gamma(\bar B_s\to
K^+\ell^-\bar\nu_\ell)=(5.45^{+0.83}_{-0.80})|V_{ub}|^2\times 10^{-9}\,{\rm
MeV}$, which is about 20\% higher than the prediction based only on QCD light
cone sum rule estimates. Differences are much larger for the $f^+$ form factor
in the region above $q^2=15$ GeV$^2$.
