  A quasi-local mass, typically defined as an integral over a spacelike
$2$-surface $\Sigma$, should encode information about the gravitational field
within a finite, extended region bounded by $\Sigma$. Therefore, in attempts to
quantize gravity, one may consider an infinite dimensional space of
$2$-surfaces instead of an infinite dimensional space of $4$-dimensional
Lorentzian spacetimes. However, existing definitions for quasilocal mass only
applies to surfaces outside an horizon whose mean curvature vector is
spacelike. In this paper, we propose an extension of the Wang-Yau quasi-local
energy/mass to surfaces with timelike mean curvature vector, including in
particular trapped surfaces. We adopt the same canonical gauge as in the
Wang-Yau quasi-local energy but allow the pulled back "killing vector" to the
physical spacetime to be spacelike. We define the new quasi-local energy along
the Hamiltonian formulation of the Wang-Yau quasi-local energy. The new
definition yields a positive definite surface energy density and a new
divergence free current. Calculations for coordinate spheres in Kerr family
spacetime are shown. In the spherical symmetric case, our definition reduces to
a previous definition \cite{lundgren2007self}.
