  We prove power-saving bounds for general Kloosterman sums on
$\operatorname{Sp}(4)$ associated to all Weyl elements via a stratification
argument coupled with $p$-adic stationary phase methods. We relate these
Kloosterman sums to the Fourier coefficients of $\operatorname{Sp}(4)$
Poincar\'e series.
