The school has faced questions over its leadership over the past two years following the departures of the former headteacher and chaplain, neither of which were fully explained. It led to accusations of "secrecy" at the school, which is run by the Diocese of Lichfield.
Twelve governors have left the school over the last year, with five coming in, leaving an almost entirely new leadership team in place. The previous chair of governors resigned the day before the inspection, Ofsted said.
Wolverhampton Council has said it is working with the school to address the issues raised.
Councillor Wendy Thompson, opposition leader in Wolverhampton and ward member for nearby Tettenhall Wightwick, said the new leaders had a big job on their hands to restore trust.
She said: "Parents need reassurance. Therefore it's extremely important this school looks very closely at this report and brings the leadership to take it forward.
"It does need to come away from the difficult period that it has had. The safeguarding issues are of particular importance. They must be a priority because parents, when they send their children to school, have got to have assurance their child will be looked after to the highest standard. No parent would want anything less."
Senior figures at Wolverhampton Council are known to have had concerns about the running of St Peter's and will be monitoring the situation closely.
Councillor Thompson added: "There have been concerns, certainly in the past. The governing body now has a very important job to do."
Meanwhile, it has emerged new headteacher Jon Arnold told colleagues upon leaving his previous school in Shrewsbury he had been "unhappy" and put under "vast pressure" while there. A letter sent before leaving the Shrewsbury Academy was leaked to sister paper the Shropshire Star in the summer.
Former headteacher David Lewis left St Peter's in December 2019 having been suspended and away from the school for the best part of a year. No reference was made to his suspension when his departure was announced.
School chaplain Reverend David Weller also had his contract terminated in February last year following a complaint. The Diocese said the departures of the two men were not connected.