Taking a basic course then target shooting on the range is not enough preparation to successfully survive a deadly force encounter. Unfortunately, most ranges are not going to allow you to work on your conceal carry draw stroke, turn lights down to work on your low light skills, move around obstacles and shoot on the move. Skill building training on use of cover, moving off the X, close encounter shooting and learning life safety skills are attained by completing a training course with an experienced instructor. Feedback from an instructor crucial to improve your skills.
Once you have mastered your foundation skills apply those skills in the context of personal protection. Reacting to a threat that is close to you, a surprise to you with risk of death or serious bodily injury is stressful. Your mind and body will react differently than your target shooting fundamentals and mindset. Do not assume you are “trained” by taking a concealed carry class. These skills are perishable that require regular dry fire or live fire practice.
Most defensive shooting incidents are over in seconds. Muscle memory training enables you to react on autopilot when confronted with a lethal threat. That response is achieved by repetitions in training and survival mindset.
Is advancing your handgun skills necessary after taking a firearms safety course or a basic handgun class? Yes.