Chemical equilibrium is a subset of thermodynamic equilibrium. So there are no examples of systems in thermodynamic equilibrium that are not also in chemical equilibrium.
Here's an example of a hypothetical system in chemical equilibrium but not in thermodynamic equilibrium. A system containing two phases, one a condensed phase containing two equilibrating chemicals having no significant volume changes accompanying the reaction, the other an inert gas phase, under varying external pressure. The system is always in thermal equilibrium with its surroundings.
This system would not be in thermodynamic equilibrium because as the external pressure changed the gas phase would be changing its volume. It remains in chemical equilibrium because the condensed phase housing the chemical equilibrium would not respond to the pressure change, and the gas phase hosts no chemical equilibria.
This is basically a cheat because the system is, practically speaking, two separate systems that are in physical contact. Maybe someone else will be more imaginative.