  We introduce and study the notion of a generalised Hecke orbit in a Shimura
variety. We define a height function on such an orbit and study its properties.
We obtain a lower bounds for the size of Galois orbits of points in a
generalised Hecke orbit in terms of these height, assuming a version of the
Mumford-Tate conjecture. We then use it to prove the generalised
Andr\'e-Pink-Zannier conjecture under this assumption by implementing the
Pila-Zannier strategy.
