I am not a specialist on substance abuse and dependence. The thoughts expressed here are informal and tentative, and I encourage you to explore these topics with true experts.
A lot depends of the total history of alcohol consumption, and personal factors such as age, weight, and gender. The long-term effects of mild consumption (in terms of weight, gender, etc.) on the brain may be fairly limited and relatively quickly reset after sobriety. Then the effects of no longer drinking would be felt more through psychosocial pathways (e.g., experiencing a loss of “fun” or stress relief) than through physiological pathways – though this is a very informal tentative uneducated view.
Long-term moderate to severe drinking (defined relative to the particular individual) could affect neurochemistry in a variety of ways, as discussed in these articles:
I doubt there is any particularly clear information about how long it takes to return key neurotransmitter systems back to their original healthy activity. It’s hard to assess neurotransmitter activity in humans . . . and how informative are invasive studies of rats? How Drugs Affect Neurotransmitters (nice current summary)
The practical takeaways from the neural implications of alcohol consumption would be in sobriety to: Find other ways to relax and lower stress (compensating for the desensitization of GABA receptors).
Find forms of enjoyment and “stimulation” that are both rewarding and relatively mellow (compensating for the hypersensitization of glutamate receptors and the disruption of dopamine activity).
Through exercise and engaging complex mental activities, encourage neurogenesis in the hippocampus (compensating for the ways that high alcohol consumption damages and kills neurons).
Through social support and other means, find ways to stay sober . . . one day at a time (compensating for the ways that alcohol consumption, especially intermittent high consumption, can alter the nucleus accumbens and other reward-seeking systems in the subcortex to crave alcohol even months or years into sobriety).
Of course, there are other useful actions in sobriety besides the neurally-informed ones noted above.