How to describe a person with no criminal record?

Solution 1:

clean

adjective (HONEST)
​C2 honest or fair, or showing that you have not done anything illegal:

The judge took the defendant's clean record (= the absence of previous involvement in crime) into account when passing sentence.

I've always had a clean driving licence.

The first cited use case should be enough to show that clean does work, although in qualifying the noun "record" not "defendant."

To extend the meaning to the person, we can use the sense of "17. honourable or respectable."

Solution 2:

Maybe law-abiding is the term you want. It doesn’t exactly mean “of someone without a criminal record,” but it does mean the person the term is describing isn’t a criminal. (Which is, essentially, the same thing.)

So, you can say, “He/She has no criminal record; he/she is law-abiding [OR] he/she is a law-abiding citizen.”