Try saddle soap.
You can use leather conditioner made for leather car upholstery. Found in the automotive section in any big box store or local home improvement store. I just cleaned my leather chair yesterday using white shaving cream-the traditional kind not the gel. Spray on rag and then rub in circular motion onto chair in small sections at a time. Wipe any residue off with a clean, dampened rag. and then buff with an old cotton dishtowel or microfiber cloth. I only used water to dampen my cleaning rag.
Hometalks How to Clean Your Leather Couch link might be informative. I hope it helps address your leather chair cleaning concerns.
Saddle soap to clean and leather conditioner to keep it soft and supple.
Use only products made to clean and condition leather only. Leather cleaner, saddle soap are good suggestions, but don't forget the leather conditioner to make sure the piece stays soft and supple.
you may find this article helpful:https://homeguides.sfgate.com/house-products-can-used-clean-leather-furniture-103465.html