Improve your posture
Some postural improvement can be brought about through corrective exercise, although my suggestion is that posture is as much, if not more, about neural adaption, than muscular. In other words, much of our postural behaviours are habits and are a product of patterns that we have learned, rather than muscles that are either tight and short or long and weak. I'm not suggesting musculoskeletal factors are not important, far from it, but I think we should look at it as a systemic issue.
Focus on corrective exercise will also help, but improving efficiency of movement, especially in the gym, will probably yield greater changes. If we take the time to do some movement re-education training and learn how to move and exercise in the right way, whilst perhaps also targeting some specific muscles, we will probably find that this this will go a long way towards alleviating any symptoms, as the right muscles start to become more active and our body becomes systemically stronger.