If you've recently become a DE resident from NJ, you'll need to submit a certified copy of your NJ driving record, so DE will certainly see the prior conviction.
If not, DE might not find the conviction, but personally I would not risk hiding it. That will likely bite you in the butt. I would call NJ motor vehicles (609-292-6500) and try to get the details necessary for the application.
P.S. if it was a DWI, it cannot be expunged. NJ has no mechanism to expunge Title 39 (motor vehicle) violations. They are there forever.