Clock keeps correct time but pendulum does not move

Check that the hands are tight and also that they are not touching. and jamming. Remove the battery and replace it. Some have a lever to give it a jolt to get moving.

https://www.google.com/search?q=Infinity+group+Pendulum+Wall+Clock

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It is a handsome longcase clock and rather elaborate - it would be disappointing to discover the weights and pendulum are merely decorative.

I have only encountered one similar clock and it had one battery to keep the pendulum swinging and another to power the clock. The battery had to be fairly fresh or the pendulum stopped swinging. The clock also had to be level or the pendulum stopped.

If you took the picture when the pendulum was stationary, the clock appears not to be standing vertically. It is important they stand vertically in both planes to the nth degree.
There is also a fable about a clock never being happy standing next to or hanging on an exterior wall, sometimes not such a fable...

I don't think the pendulum is the problem. I suggest you should level the clock (considering the shape of the case a plumbline would be best), fit a new battery and give the pendulum a swing - if it doesn't keep swinging, there is probably a fault with the motor.

To restart your Marcel Hour Strike Quartz Clock NRMS603, follow these steps:

Stop the Pendulum: Gently stop the pendulum from swinging by holding it still.
Remove the Battery: Open the clock case and locate the battery compartment. Remove the existing battery.
Wait for a Minute: Leave the clock without a battery for about a minute to allow any residual charge to dissipate.
Insert a New Battery: Insert a fresh battery into the compartment, ensuring the correct polarity (usually marked on the battery holder).
Start the Pendulum: Gently release the pendulum and let it start swinging.
Set the Time: Use the clock's time-setting knob or buttons to adjust the time to the correct hour and minute.
Your clock should now be restarted and keeping time accurately

probably find that the clock has it's own aa battery
the pendulum has it's own aa battery and the chimes have 2 aa batteries

Hi Pam,
I have a Howard Miller Grandfather clock and the pendulum swings very slowly and from far left to far right travels only about three inches at best. It doesn't need to move any more than that to make the "Verge" move the "Escape Wheel" to rotate the gears to keep the hands moving at the correct tick.
Howard Miller Grandfather Clock

Hi Pam,
I have a Howard Miller Grandfather clock and the pendulum swings very slowly and from far left to far right travels only about three inches at best. It doesn't need to move any more than that to make the "Verge" move the "Escape Wheel" to rotate the gears to keep the hands moving at the correct tick. Howard Miller Grandfather Clock

I would start by ensuring the timing or beat is set correctly. This link will walk you through the process:
How to Set the Timing or Beat on Mantel Clock

Good details! Go to Timesavers.com
You can find a replacement pendulum unit there. Your pendulum mechanism probably has a bad coil. The coil is extremely difficult to repair.

Most grandfather/grandmother clocks have an adjustable screw on the weight to slightly extend it or shorten it to satisfy the equation of pendulum swing. the shorter the swing (arc distance) the faster the clock, the longer the swing the longer the time. Check to see if you can adjust the weight up or down on the hanger.

Everybody should know that the coaster clocks discussed here run on batteries. The timing mechanisms, the chimes as well as the pendulum all are powered by a battery. Changing the speed of the pendulum is impossible because there is no adjustment. Besides, it wouldn't matter anyway. The pendulum has now affect on the clock's ability to keep accurate time. It is purely aesthetic. This is a pretty cool looking clock and even has weights, but those are also purely aesthetic and do not move the way a classic grandfather clock weight would move. The moments with these clocks are not designed to be worked on. These clocks are relatively inexpensive (approximately $300) but do add a nice look to your home. Grandfather clocks snobs would say though; this is not a true timepiece. They're right... Sorry.