As a Head of School, in 4 different countries, I have encountered this twice.

1, A new teacher was honest and said he had a criminal record upfront, it was for a drunken binge on his graduation night and he smashed a window. Fine was accepted and no further issues.

2, Was a bit more complicated, it came to light that one of my staff had not supplied a full Disclosure only Basic Disclosure, which only gives unspent convictions. On investigation, it actually showed that this person had three convictions for Fraud and had spent a number of years in her majesty's prisons. Although many of the convictions were to run concurrently, the total number of years was in double figures. I fired that person immediately, what would parents say if they found out, should it come to light. Also the person tried to cover it up with a basic Disclosure.

Best advice, be upfront and admit your error, better that way than waiting to be caught.