  Let $\alpha\in(0,2)$ and $d\in\mathbb{N}$. Consider the following SDE in
$\mathbb{R}^d$:$$\mathrm{d} X_t = b(t,X_t)\mathrm{d} t + a(t,X_{t-})\mathrm{d}
L^{(\alpha)}_t,\ \ X_0 = x,$$where $L^{(\alpha)}$ is a $d$-dimensional
rotationally invariant $\alpha$-stable process, $b:\mathbb{R}_ +
\times\mathbb{R}^d \to\mathbb{R}^d$ and $a:\mathbb{R}_+ \times \mathbb{R}^d \to
\mathbb{R}^d \otimes \mathbb{R}^d$ are H\''older continuous functions in space,
with respective order $\beta,\gamma\in (0,1)$ such that $(\beta\wedge
\gamma)+\alpha>1$, uniformly in $t$. Here $b$ may be unbounded.When $a$ is
bounded and uniformly elliptic, we show that the unique solution $X_t(x)$ of
the above SDE admits a continuous density, which enjoys sharp two-sided
estimates. We also establish sharp upper-bound for the logarithmic derivative.
{In particular, we cover the whole \textit{supercritical} range $\alpha\in
(0,1)$.} Our proof is based on \textit{ad hoc} parametrix expansions and
probabilistic techniques.
