  We propose a symmetry of $T\bar T$ deformed 2D CFT, which preserves the trace
relation. The deformed conformal killing equation is obtained. Once we consider
the background metric runs with the deformation parameter $\mu$, the
deformation contributes an additional term in conformal killing equation, which
plays the role of renormalization group flow of metric. The conformal symmetry
coincides with the fixed point. On the gravity side, this deformed conformal
killing equation can be described by a new boundary condition of AdS$_3$. In
addition, based on the deformed conformal killing equation, we derive that the
stress tensor of the deformed CFT equals to Brown-York's quasilocal stress
tensor on a finite boundary with a counterterm. For a specific example, BTZ
black hole, we get $T\bar T$ deformed conformal killing vectors and the
associated conserved charges are also studied.
