Who did you replace as a teacher? A beloved teacher or one that did not have many fans. In my career, I have had the opportunity to replace one of each.
In my first position, I replaced a teacher that did not have a lot of fans. I discovered this from a friend who attended the school and whose brother was one of my first students. My friend shared this nugget of truth,
"The students are going to love you for the first 4 months because you are not her, after that, they are going to base everything in the classroom on you."
And he was right. Everything I tried was golden. Students enthusiastically became involved in every simulation or project I proposed. Classroom management was easy (at least for what it could be for a first year teacher).
And then...the fall.
My biggest mistake was that I took for granted this gift rather than using it to build structure, organization, and boundaries in my classroom. From January on I struggled controlling my classroom. Students began questioning what I was doing in my classroom. My authority was challenged daily. Basically, I experienced everything a first year teacher typically does, just a bit delayed. If you find yourself replacing the teacher who had few fans, don't skate the first few months thinking the season of adulation had anything to do with you. Work as hard as any first year teacher in establishing routines and commanding respect, because with all seasons, it will come to an end.
In my second position, I replaced a beloved and highly honored teacher. In fact, on a visitation the day before school, a parent said to me
"I'm sure you're a good teacher, but we would much rather have (old teacher's name) be our daughter's teacher. No offense"
One advantage I had in the second situation is that I had seven years of teaching history under my belt. The other advantage was that the old teacher was still in the district, and the reason he was a beloved teacher was because he was one of the nicest men I have ever met. He would encourage me by providing feedback and advice on my classroom.
If you find yourself in this situation see if the previous teacher would like to stay in correspondence with you. (If they choose not to, or find it an annoyance, drop it). Ask teachers who worked with the old teacher what their strengths and weaknesses were. Maintain some traditions of the old classroom. Remember, there was a reason why that teacher was beloved and highly respected. Don't think you can come in as a maverick and change everything. Many students who had older siblings that had the old teacher (and more importantly their parents) will appreciate the nod you are giving the former teacher and will establish a level of comfort for them.
However you ARE NOT that beloved teacher. You need to make a mark of your own. For me, it was developing a Presidential Election Game and Project for the 2000 U.S. Presidential election. It even spurred a reporter from the local newspaper to contact me to discuss what we were doing in class. At the end of the year, the parent from above apologized for what she said and even went as far as thanking me for a wonderful year.
Very similarly to the teacher with not a lot of fans, eventually you are going to step out of the shadows of the beloved teacher and be judged on your merits.
So be BOLD and be EXCELLENT!