  Inspired by the first observation of a vector charmonium-like state $Y(4626)$
decaying to a meson pair $D_{s}^{+}D_{s1}(2536)^{-}$, which could be viewed as
a $P$-wave scalar-scalar $[cs][\bar{c}\bar{s}]$ tetraquark state, we predict a
potential vector charmonium-like state $Y$ with $P$-wave scalar-scalar
$[cq][\bar{c}\bar{q}]$ configuration. The corresponding mass spectrum of $Y$
state is calculated to be $4.33^{+0.16}_{-0.23}~\mbox{GeV}$ in the framework of
QCD sum rules. We suggest that the predicted $Y$ state could be looked for in
an open-charm $e^{+}e^{-}\rightarrow\bar{D}D_{1}(2420)+c.c.$ process.
