It changes.
Without external electric or magnetic fields, for most energy levels, there are several "orbits" (wave functions or simply states is a better word) that have the same energy (they are called "degenerate"). You can combine these in any way you want without changing the energy of the new state. Now if you add an external field, magnetic or electric or both, the energies of these states do become different (they split). You then have to find the "right" combination of states that solves the Schroedinger equation (or whatever model you use), i.e. find Eigenstates of the Hamiltonian that have a defined energy. Symmetry is an important help for doing that.
Now if the energies of the states change, then the energy difference between two states changes, too. This energy difference is probably what you refer to as "energy required for an electron to change orbit".