Ms Collins is due to step down at the end of April “to face some new health challenges”.
It has been well documented previously that she has battled breast cancer dating back more than a decade.
Addressing West Yorkshire's Police and Crime Panel (PCP) on Friday, Mr Burns-Williamson said he believed it is worth spending the extra time to find the right person for the job.
He said: “I will be wanting to attract a wide number of candidates for the job and will use a number of measures including psychometric testing in the process.
"We're in no rush to find a replacement. I want to get the appointment right."
The PCC added he was confident that the chief officer team can take on the further responsibility while a suitable replacement is found.
Paying tribute to his departing colleague's work, he added: “She took over at a difficult time and has done a fantastic job and has had such a positive impact on policing in West Yorkshire.”
Ms Collins has served 31 years in policing and was awarded a Queen's Police Medal in 2013 and a CBE for services to policing last year.
Looking back on her time with the police force, she said: "I have tried to encourage an understanding of the very human aspects of policing, with a culture that truly cares about our communities.”
Leeds councillor Alison Lowe, chairing her last PCP today before stepping down as an elected member for Armley, said she hoped Ms Collins' replacement will be as effective as she has been.
She said: “We just hope her replacement will be as honest and transparent as she has been.
“We completely understand why she is stepping down, and we wish her all the best in the future.”