Sometimes I feel like a broken record when I say that young athletes don't get very good instruction (or any at all) in weight lifting. Yet if you look around at the majority of high schools, you will see hundreds of athletes who are benching, squatting, deadlifting, overhead pressing, or performing olympic lifts with absolutely no idea of proper form. Furthermore, I'd be willing to bet most of them haven't gone through any type of pre-participation weight lifting screening.
Overhead pressing is one of those exercises that get abused with athletes and even the general population who are not appropriate for them. Understand when I say appropriate, that means functionally able to perform that exercise safely and with correct/proper form.
In this article, Tony Gentilcore of Cressey Performance, breaks down overhead pressing. He explains what specific assessments can help aid your clients in determining if they are functionally able to overhead press. Additionally, he gives his input as to why each assessment is indicative of being physically ready to overhead press. Can't overhead press? Tony gives you videos on what you can do to substitute for the overhead press.
Don't put strength on top of dysfunction. Assess your athletes before prescribing the overhead press. It will make you look like a genius and help save that athlete a headache and rehabilitation later.