We introduce a novel framework, rooted in the generalized unitarity methods of scattering amplitudes, to study high-order gravitational effects on a binary from the scattering of its emitted gravitational radiation. Here we focus on the radiation reaction due to the background of the binary’s gravitational potential, namely on the so-called tail effects, as the starting point to study these types of scattering. We start from the effective field theory (EFT) that treats the binary as a composite particle. Through multi-loop and generalized unitarity methods, we derive the causal effective actions of the dynamical multipoles, the energy spectra, and the observable flux, due to these effects. We proceed through the third subleading such radiation-reaction effect, at the four-loop level and seventh order in post-Newtonian gravity. This order is beyond what has been previously attempted via EFT approaches, and competitive with traditional GR calculations.