Yes, according to Einstein's theory of general relativity, time moves slower in regions with stronger gravitational fields. This phenomenon is known as gravitational time dilation.
The theory states that the presence of a massive object, such as a planet or a black hole, curves the surrounding spacetime. This curvature affects the flow of time, causing it to pass more slowly in the vicinity of strong gravitational fields compared to regions with weaker fields.
Therefore, on a planet with higher gravity, time would indeed pass more slowly relative to a planet with lower gravity. This effect has been observed and measured in various experiments and observations, including the famous Hafele-Keating experiment conducted in the 1970s using atomic clocks on airplanes.
It's worth noting that the time dilation effect due to gravity is relatively small in everyday situations. However, it becomes more pronounced near extremely massive objects like black holes or in scenarios involving high velocities.