If someone's permit has expired, do they have to take the written test again, or can they just renew their permit.

You gotta take the test again.

Your written test is good for 1yr. As long as that hasn't expired you can renew the permit without retaking the written. Your allowed 2 permits, (6mo each) each time you take the test. So you'll be required to take the test again if you try to get a 3rd permit or if its been over 1yr since you've had a passed test.

Well it depends on if they're in between their 30-day grace period . They don't take it but if it's past you have to retake it .