Hi Anne,
I am not familiar with the expression "clean chit".
You can "keep a clean sheet", or "keep the slate clean" which means make no mistakes
And you can start again by starting with a clean sheet, or as you say, clean slate.
Here is an example from the Guardian newspaper:
"It's clean sheet time. We are starting afresh, and I think Lawton has done a very good job. She is a very decent and honest person and I think she has had a battle with the way the whole place is structured.
"But I think she has moved it on quite a bit, and now she wants to go and let someone else take up the cudgels."