I don't know what parliamentary precedent Mrs. Atwin is referring to, but chiefs of staff—current chiefs of staff, former chiefs of staff—are not immune from attending a committee.
As a case in point, we had Katie Telford, the Prime Minister's chief of staff, attend not too long ago for a two-hour meeting. It doesn't get much higher than Katie Telford. Again, I challenge Mrs. Atwin to provide some evidence of some parliamentary precedent that has been set that the Conservatives are no longer following.