  Let $F $ be a totally real number field and $r=[F :\mathbb{Q}].$ Let
$A_k(\mathfrak{N},\omega) $ be the space of holomorphic Hilbert cusp forms with
respect to $K_1(\mathfrak{N})$, weight $k=(k_1,\,...\,,k_r)$ with $k_j>2,$ for
all $j$ and central Hecke character $\omega$. For a fixed level $\mathfrak{N},
$ we study the behavior of the Petersson trace formula for
$A_k(\mathfrak{N},\omega)$ as $k_0\rightarrow\infty$ where
$k_0=\min(k_1,\,...\,,k_r)$. We give an asymptotic formula for the Petersson
formula. As an application, we obtain a variant of a discrepancy result for
classical cusp forms by Jung and Sardari for the space $A_k(\mathfrak{N},1),$
where the ring of integers $\mathcal{O}$ has narrow class number $1$, and the
ideal $\mathfrak{N}$ is generated by integers.
