For most recovering alcoholics it is important for them to avoid things such as social interactions and social situations which trigger cravings for alcohol.
A relationship with an alcoholic isn't impossible, but it does take a certain finesse.
I'm kind of a private person myself, and I don't want to offend him or seem like I'm prying.
Beyond the fact that he's been sober for 4 years, I know nothing about what he went through, when he realized he needed to get sober, or anything about the process.
Be aware of the triggers the person you are dating has told you about.
Offer your support by helping her to avoid these triggers. Understand how alcoholism shows up in his life and the measures you have to take.