  In this paper, we investigate the hypergraph Tur\'an number
$ex(n,K^{(r)}_{s,t})$. Here, $K^{(r)}_{s,t}$ denotes the $r$-uniform hypergraph
with vertex set $\left(\cup_{i\in [t]}X_i\right)\cup Y$ and edge set $\{X_i\cup
\{y\}: i\in [t], y\in Y\}$, where $X_1,X_2,\cdots,X_t$ are $t$ pairwise
disjoint sets of size $r-1$ and $Y$ is a set of size $s$ disjoint from each
$X_i$. This study was initially explored by Erd\H{o}s and has since received
substantial attention in research. Recent advancements by Brada\v{c},
Gishboliner, Janzer and Sudakov have greatly contributed to a better
understanding of this problem. They proved that
$ex(n,K_{s,t}^{(r)})=O_{s,t}(n^{r-\frac{1}{s-1}})$ holds for any $r\geq 3$ and
$s,t\geq 2$. They also provided constructions illustrating the tightness of
this bound if $r\geq 4$ is {\it even} and $t\gg s\geq 2$. Furthermore, they
proved that $ex(n,K_{s,t}^{(3)})=O_{s,t}(n^{3-\frac{1}{s-1}-\varepsilon_s})$
holds for $s\geq 3$ and some $\epsilon_s>0$. Addressing this intriguing
discrepancy between the behavior of this number for $r=3$ and the even cases,
Brada\v{c} et al. post a question of whether \begin{equation*}
\mbox{$ex(n,K_{s,t}^{(r)})= O_{r,s,t}(n^{r-\frac{1}{s-1}- \varepsilon})$ holds
for odd $r\geq 5$ and any $s\geq 3$.} \end{equation*}
  In this paper, we provide an affirmative answer to this question, utilizing
novel techniques to identify regular and dense substructures. This result
highlights a rare instance in hypergraph Tur\'an problems where the solution
depends on the parity of the uniformity.
