You learned that 付き合う means "to keep company with," and this is its noun version. When you keep company with someone, you have an association or a relationship with them.

付き合い refers to ongoing interactions or connections with people, like 人付き合い (social relationships) or 長い付き合い (a longstanding association). It can also refer to the obligations that result from such relationships, like 付き合いで飲みに行く (go drinking out of social obligation). You may not want to go, but… society demands it.

You'll also sometimes see it with the honorific お, as in お付き合い — especially when referring to business associations or respectfully talking about romantic relationships.

The reading comes from 付き合う, so if you know that, you should be fine here.