When should I give my job notice?

Hi All- I’m a veterinarian and have accepted a new, industry position. I wanted to give my new clinic a month notice but the new job has a background check process. I do not do drugs or have a criminal past (except a DWI 16 years ago in college) but I’m always paranoid about these things. I really don’t think I have anything to be afraid of. Should I wait until I pass the background checks before I give notice? I’m just a little concerned it might take some time and I’ll only be able to give my current employers a few days/2 weeks.

Thanks!

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