There is a set of expectations for every team. You would hope they would be well defined, reasonable, and achievable. You would hope that existing systems, processes, reports and documentation would support the team in fulfilling those expectations.
Of course, if that was the case there would be nothing for me to do.
You have to figure out - as quickly as possible - what the organization expects of your team. This is hard because different people will have different ideas of your mission, responsibilities, and capabilities. Other teams or executives may use the time of transition to add scope - team members may try to reduce scope. It's your job to figure out what the team can and should be responsible for. Pay particular and immediate attention to any SLAs.
Meet with your team - inventory the tasks, deliverables, reports, and documentation. Don't be surprised to find this stuff scattered around, non-existent, or not forthcoming. The longer the team has been in existence and working together the harder it will be to get even simple things like a complete list of tasks and deliverables.
You're going to have to dig in and sit with people to see what they are really doing. You will often find that the person doing some ten-step procedure to overcome a common issue does not even recognize it as a task - it's just something you have to do... Same for deliverables; people might produce and distribute needed work product without recognizing it as a required deliverable.
Figuring out everything that your team does takes a lot longer than you might expect - keep looking, send people on vacation, question everything that seems like it should be on the list but isn't. Why is Joe Blow asking for that from us?
Meet with your boss(es) - try to understand their idea of your mission. Get copies of any deliverables they routinely receive from your team. Talk about success criteria - expect this to be something very helpful like "be perfect", "100 percent error free", or "Make sure nobody escalates to me." If you're very lucky you will get some objective criteria that is both within your control and something you can measure.
Something to be on guard for is bogus reporting from your predecessor and areas where the picture has been presented very carefully, giving the impression of more capability than really exists. This stuff can make your job a lot harder, and your life miserable when it takes you by surprise. I have taken over an area only to be asked for a recurring report that nobody on the team has any idea how to produce - and has shown improvement. Upon further investigation all I could determine was that the guy was making up the numbers. Worse, the numbers he was reporting on would not measure the team's effectiveness.
Meet with your customers - anybody that expects your team to produce work product, perform tasks, etc. is your customer. Find out what they think your team does and make sure you capture any sort of report or other deliverable. As you develop the relationship your customers will become your allies - but you have to make sure you know what they need, why they need it, and what they do with it.
Almost assuredly your team, bosses, and customers are on different pages or even reading different books. All the work in the world won't lead to success if what you deliver is not what they expect.
Thanks for reading - Mike