  We present an elementary uniform lower bound for the classical Kloosterman
sum $S(a,b;c)$ under the condition of its non-vanishing and $(ab,c)=1$, with
$c$ being an odd integer. We then apply this lower bound for Kloosterman sums
to derive an explicit lower bound in the Petersson's trace formula, subject to
a pertinent condition. Consequently, we achieve a modified version of a theorem
by Jung and Sardari, wherein the parameters $k$ and $N$ are permitted to vary
independently.
