No, you cannot obtain a driver's license in Florida while your license is suspended in New Jersey. According to the Florida driver's handbook you cannot obtain a FL driver's license with a suspended license in any another state. The handbook states that driving a motor vehicle in Florida is a privilege you earn. You cannot obtain a license in Florida under the following conditions:
- If your license is suspended or revoked in any state;
- If you are addicted to drugs or alcohol;
- If you cannot drive safely because of mental or physical problems; (Deafness alone will not prevent a person from being issued a driver license.)
- If you are under the legal age for licensing (15 for Learner's license, 16 for Class E).
The Florida Department of Highway Safety and Motor Vehicles (HSMV), the state agency that grants driver's licenses for FL, notes that on the application for the license it is asked whether the applicant has previously been licensed to drive, and, if so, when and by what state, and whether any such license or driving privilege has ever been disqualified, revoked, or suspended, or whether an application has ever been refused, and, if so, the date of and reason for such disqualification, suspension, revocation, or refusal.
[Let CarInsurance.com help you find affordable auto insurance now.] You could not just leave off information about your suspended NJ license from the Florida driver's license application because the FL HSMV would check the National Diver Register (NDR) and find out about this suspension. All states input information about "problem drivers" into the NDR and all states check the NDR when a person applies for a license. Your NJ suspended license will be listed in the NDR by the New Jersey MVC.
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If you somehow were able to acquire a Florida license but did not mention the NJ suspension and Florida later found out your FL license would be cancelled. The HSMV states that if your license was issued because of a mistake or fraud (giving false information or identification), it will be cancelled.
To obtain a Florida driver's license you would need to be able to reinstate your NJ license. If this is not possible you can contact the FL HSMV to see if there are any options for you such as a hardship license to get to work.
When you are able to obtain a full, valid license you can come to use for free auto insurance quotes online. | 
