Partner with your clients and delivery teams
My first recommendation should not be a surprise to anybody. Regardless how good you are from a technical perspective, you will be unable to succeed as a great production support leader if you fail to partner with your clients and IT delivery teams.
You have to realize that you are providing a service to your client who is the owner and master of the IT production environment. You are expected to ensure the availability of the critical Java EE production systems and address known and future problems to come. Stay away from damaging attitudes such as a false impression that you are the actual owner or getting frustrated at your client for lack of understanding of a problem etc. Your job is to get all the facts right and provide good recommendations to your clients so they can make the right decisions. Over time, a solid trust will be established between you and your client with great benefits & opportunities.
Building a strong relationship with the IT delivery team is also very important. The delivery team, which includes IT architects, project managers and technical resources, is seen as the team of experts responsible to build and enhance the Java EE production environments via their established project delivery model. Over the years, I have seen several examples of friction between these 2 actors. The support team tends to be over critical of the delivery team work due to bad experience with failed deployments, surge of production incidents etc. I have also noticed examples where the delivery team tends to lack confidence in support team capabilities again due to bad experience in the context of failed deployments or lack of proper root cause analysis or technical knowledge etc.
As a production support individual, you have to build your credibility and stay away from negative and non-professional attitude. Building credibility means hard work, proper gathering of facts, technical & root cause analysis, showing interest in learning a new solution etc. This will increase the trust with the delivery team and allow you to gain significant exposure and experience in long term. Ultimately, you will be able to work and provide consultation for both teams.

Proper balance and professionalism between these 3 actors is key for any successful IT production environment.