My anxiety really kicked in full force about 2 years into my recovery. I've always had it and it was strong towards the end of my drinking too, and while quitting helped it never went away.
For me it's been a combination of therapy, mindfulness/meditation, excercise and acceptance. By that I mean I have had to simply accept that I'm an anxious person. That doesn't mean that there is nothing I can do about my anxiety, and it doesn't mean that I don't feel a LOT better now than I did before - but some days I'm just anxious. It's woven into the "fabric of me" just like my addiction is.