Pearl rings can be challenging to clean. If the pearl is set with diamonds, it can be hard to keep them sparkly without harming the pearl.

I recommend taking rings like that to a professional jeweler to be cleaned.

Or try a very mild dish soap, warm water and a soft bristle toothbrush to clean the stones and setting. Do not use the brush on the pearl. Use only warm water to remove any dirt on the pearl. Wipe the pearl clean with a soft non abrasive cloth to avoid scratches.
Never use jewelry cleaner on pearl jewelry. It will remove the lustre and you can never get it back once it is damaged.