  We investigate higher-order corrections to correlators in a general CFT with
the double trace $T\bar{T}$ deformation. Traditional perturbation theory proves
inadequate for addressing this issue, due to the intricate stress tensor flow
induced by the deformation. To tackle this challenge, we introduce a novel
technique termed the conservation equation method. This method leverages the
trace relation and conservation property of the stress tensor to establish
relationships between higher and lower-order corrections and subsequently
determine the correlators by enforcing symmetry properties. As an illustration,
we compute both first and higher-order corrections, demonstrating the impact of
stress tensor deformation on correlators in a general deformed CFT. Our results
align with existing calculations in the literature.
