The Bishop of Gloucester, Rt Revd Rachel Treweek said immoderate bishop reasoning astir becoming the Archbishop of Canterbury needs "their caput reading".
Justin Welby will measurement down aft a damning study into prolific kid abuser John Smyth associated with the Church of England.
Bishop Rachel told BBC Radio Gloucestershire she did not privation the "very, precise hard job" and immoderate Bishop reasoning astir it should "look agelong and hard into the reflector and instrumentality immoderate world checks".
She said Mr Welby's determination was "absolutely the close happening to do" but that it "probably could person happened quicker".
The study recovered that Mr Welby "could and should" person reported Smyth's maltreatment of boys and young men to constabulary successful 2013.
It was not instantly wide erstwhile the archbishop would permission his station but the process of uncovering a replacement is apt to instrumentality astatine slightest six months.
The Archbishop of Canterbury is the caput of the Church of England and leads 85 cardinal Anglicans successful 165 countries astir the world.
"Anyone who wants to beryllium the Archbishop of Canterbury perfectly needs their caput reading," Bishop Rachel said.
"You know, this is simply a very, precise hard occupation - stepping into the structures that bash request to change.
"Any bishop who wants to beryllium the archbishop, well, I deliberation they mightiness request to look agelong and hard into the reflector and instrumentality immoderate world checks."
Smyth was accused of attacking dozens of boys, including those helium met astatine Christian camps, successful the UK successful the 1970s and 1980s.
The independent report published past week recovered inaction from the Church was a "missed opportunity" to bring Smyth to justness earlier his decease successful 2018.
The Bishop called it an "absolutely sickening report", adding the absorption needs to beryllium connected the victims and survivors who had had to hold years for the maltreatment to beryllium afloat exposed.
"I privation to instil spot and religion and accidental to victims and survivors that if you person been silenced, if you are carrying that value today, past delight bash interaction your diocesan safeguarding team," she said.
She said safeguarding processes and grooming wrong the Church had changed successful caller years but autarkic oversight was needed.
"One of the things that this study and consequent events has thrown up again is the precise clunky governance we person wrong the Church of England," she added.
"We bash not person speedy determination making, determination are excessively galore antithetic levels, groups, involved.
"We request to beryllium capable to determination overmuch much swiftly."
Bishop Rachel was consecrated arsenic the 41st Bishop of Gloucester successful 2015.
She made past by becoming the archetypal pistillate diocesan bishop and the archetypal pistillate bishop successful the House of Lords.