As you are aware in Minnesota carpool lanes or HOV lanes are restricted to vehicles with two or more occupants. They are marked by a diamond symbol or with "Carpool Only" signs. They are usually located on the far left side of a freeway and are separated from other traffic lanes by combinations of white or yellow lines.
Section 171.12 of the Minnesota Statutes deals directly and specifically with the MN driving records.
Subsection 3 notes that the driver's record pertaining to revocations, suspensions, cancellations, disqualifications, convictions, and accidents is cumulative and must be kept for a period of at least five years. Furthermore the driver's record pertaining to violations of a driver or vehicle out-of-service order must be kept for a period of at least ten years.
The driver's record pertaining to felony convictions in the commission of which a motor vehicle was used and certain alcohol-related offenses and licensing actions listed are permanently retained on the record.
Since the MN law is a bit wordy and seems unclear if violations, such as your HOV lane offense, are kept on your record for 5 or 10 years we contacted the Minnesota Driver and Vehicles Services. Their representative stated that the retention length depends on the type of violation.
She went on to say that regular moving violations (speed, stop signs, HOV, etc) have a 5 year mandatory retention under state law. After that length of time they are removable upon request. Alcohol violations however are permanent.
So the least amount of time that the HOV traffic ticket will appear on your Minnesota driving record is 5 years. If after that amount of time has passed you wish it to be taken off you will need to contact the MN driver and vehicle services department and request that it be taken off.
Thus with only 3 years elapsing since you were convicted of the HOV lane violation it will still be on your record for at least 2 more years before you can call and request it to be removed. If this is the only infraction on your driving record then it may continue to not affect your rates with your current carrier, even with a new car being placed on the policy.
If you plan to shop around with other insurance carriers when you buy the new car then it will depend upon the rating system of the individual insurance company if this violation will affect your rates or not. Some may rate on it while others may not. Insurance companies tend to "look back" on your Motor Vehicle Record (MVR) 3, 5 or 7 years so they would see it.
For more information on your driving record or on MN driving record laws contact the MN DPS.