TL;DR
Play around your energy, save your E for saving allies, reload and position yourself before your Grav, don't feel obliged to only get 4 or more in every grav.
Play around your energy. Don't be too aggressive just because you have high energy. It's better to survive with high energy than to die and lose it all.
Also, once you reach 60+ energy, save your projected barrier (E) for saving allies rather than for gaining energy. Use your Shift for that.
Before you grav, reload (if you can) and try and position yourself according to their team comp. For example, if they have a Rein, you would want to be able to get behind them so that the Rein would either have to shield your damage, or your team's damage.
When hitting people in a Grav, alternate between your primary and secondary fire, as this maximises your damage output.
(Situational) If they have a D'va or Roadhog, focus them for easy ult charge, unless you have other targets you need to prioritise.
Your ult isn't always needed as an engage to combo a bunch of ults etc.
Remember that you can use your ult to cancel an enemy teams engage before the team fight even begins. If you can successfully stop their engage, then your job is done.
When it comes to your ult, you don't need always get 4+ more people.
Don't be afraid to use it on, say, an ulting Genji to save your supports.
