  We present a generalization of the Time Dependent Variational Principle
(TDVP) to any finite sized loop-free tensor network. The major advantage of
TDVP is that it can be employed as long as a representation of the Hamiltonian
in the same tensor network structure that encodes the state is available.
Often, such a representation can be found also for long-range terms in the
Hamiltonian. As an application we use TDVP for the Fork Tensor Product States
tensor network for multi-orbital Anderson impurity models. We demonstrate that
TDVP allows to account for off-diagonal hybridizations in the bath which are
relevant when spin-orbit coupling effects are important, or when distortions of
the crystal lattice are present.
