  The notion of tamed Dirichlet space was proposed by Erbar, Rigoni, Sturm and
Tamanini as a Dirichlet space having a weak form of Bakry-\'Emery curvature
lower bounds in distribution sense. After their work, Braun established a
vector calculus for it, in particular, the space of $L^2$-normed
$L^{\infty}$-module describing vector fields, $1$-forms, Hessian in
$L^2$-sense. In this framework, we establish the Hess-Schrader-Uhlenbrock
inequality for $1$-forms as an element of $L^2$-cotangent module (an
$L^2$-normed $L^{\infty}$-module), which extends the Hess-Schrader-Uhlenbrock
inequality by Braun under an additional condition.
