As a mid-level manager, I need to manage my teams while also managing the expectations of senior managers. This in many ways is the classic dilemma of a middle manager: you are often the fulcrum point between what your teams can realistically deliver, and what others expect them to deliver.
The terminology often used to define this is "managing up" and "managing down". It is not a new concept, and has been written about extensively in business literature. 1
One pitfall that I often see my peers falling into is focusing too much effort managing in one direction to the detriment of the other. Typically you will see managers spending more time managing up via status meetings and progress reports, essentially reporting success, while losing focus on the actual deliveries happening in their teams. I tend to suffer from the opposite problem as a former engineer, namely focusing too deeply on the delivery while neglecting to promote my relationships with senior managers.
So what are some of the benefits of each approach?
Ultimately in an organization you need to promote your work, your teams work, and the value you are adding to the business. This is especially important in larger organizations, where great work can often go unnoticed. If you can prove to your senior managers that you can be an effective leader, you should be rewarded with greater responsibilities. You cannot progress without making a good impression.
If you build trust in your teams, they will reward you with hard work and loyalty. A manager's success should be judged by the success of their teams. To earn that trust, your teams need to see you supporting them publicly, advocating their work by giving them full credit and praise, and protecting them from distractions so that they can get on with their core activities. You cannot progress without engendering trust and loyalty.
The optics of your management style is important: if you spend too much time managing down, you can seem narrowly focused and insular to those outside your group. If you spend too much time managing up, you can seem to be self-promotional and political. It is very important to strike a balance, which takes skill and experience. Try to identify a fellow manager in your organization who successful does both (you can spot them as they will be liked and respected at all levels of the organization), then try to follow their lead, or better yet become their mentee if they are amenable to that.