  We consider the $T\bar{T}$ deformation of two dimensional Yang--Mills theory
on general curved backgrounds. We compute the deformed partition function
through an integral transformation over frame fields weighted by a Gaussian
kernel. We show that this partition function satisfies a flow equation which
has been derived previously in the literature, which now holds on general
backgrounds. We connect ambiguities associated to first derivative terms in the
flow equation to the normalization of the functional integral over frame
fields. We then compute the entanglement entropy for a general state in the
theory. The connection to the string theoretic description of the theory is
also investigated.
