It is said that Earth shape is roughly gravitational equi-potential surface and clock rate change due to change of the radius of rotation is compensated. But the tangential velocity component orientation differs wrt the direction of velocity relative to Milky Way centre hence clock rates should vary with longitude and sidereal time of the day.
The question comes to me in the context of Torr-Kolen experiment:
Article An experiment to measure the one-way velocity of propagation...
In this experiment two clock on the Earth's surface located on at the same latitude are assumed to have constant phase difference that is not changing while the Earth is rotating. It means that those clock relative rates remain consant.