How do you get rid of skin discoloring due to holding and smoking cigarettes?

Smoking stains: Continued smoking cessation remains the best way to get rid of skin discoloration from smoking cigarettes, as well as improving your overall health. Skin discoloration should fade over time with avoidance of the culprit (cigarettes), as the stained skin sloughs off naturally. Avoid use of harsh solvents in attempts to remove stains, as these can irritate & damage the skin.

Dunno: Sometimes skin is essentially permanently discolored in very heavy smokers, but most of the time it gradually decreases on its own. Vitamin e creams are often use to lighten skin, and there are other commercially available products, and dermatologists have prescription creams/ointments that may help. I would just give it time, congrats on quitting and hope you stay that way.