You have indicated the current loan obligation on the old vehicle is approx. $16,000. The trade market value of your vehicle is estimated at $13,000. So, you have a deficiency of approx $3,000. There are 2 remedies here;
1) pay the deficiency in cash to negate your obligation. This only suggested IF you have the excess cash. DO NOT do this if you need to borrow this money or use an operating bank line. Both of the latter will charge higher interest rates than the new vehicle lease interest rate.
2) Roll the deficiency into the new vehicle lease. Depending on the brand of new vehicle i.e. Honda Civic, the interest rates can be as low as .99%.
So rolling the deficiency from the old car into the cost of the new vehicle is allowing you to finance the deficiency at a very low interest rate with the total deficiency absorbed as you drive your new vehicle.