If you want to maximize both shoulder strength and hypertrophy, you have to maximize mechanical tension (weight). No other movement allows you to do that more effectively than the standing overhead press (OHP).
The OHP is the gold standard of overhead strength. If you want to start pressing heavier weight overhead right now, use these three tips:
1. Wear a Belt
If you want to lift as much weight as possible, you must maximize full-body tension. A lifting belt allows you to do just that. By maximizing tension and bracing effectively, you're able to recruit more motor units and incorporate more muscle into the lift, allowing you to lift more weight.
2. Maximize Tension in Your Upper Back and Lats
A strong upper back is key to pressing big weights. Your upper back musculature serves as a launch pad, and the larger and more stable the launch pad, the more weight you can press.
So before you unrack the bar, squeeze your shoulder blades together and get as much tension through the traps, rear delts, rhomboids, and upper lats as possible. This simple cue can help you immediately create a more stable launch pad to press from.
3. Lean Back as You Press
Your body naturally figures out how to lift the most weight possible, and leaning back (arching your back) allows you to incorporate more of your upper back and upper chest into the lift.
Now, some people may say this is bad for your back, but as long as you're wearing a belt and effectively bracing while maintaining full body tension, leaning back is a perfectly safe and natural movement pattern. Keep in mind, the objective is to lift as much weight as possible overhead, not to look pretty while doing it.