If you receive $16,000 for the vehicle that was fully depreciated you will have ordinary income of $16,000 in addition to your other income. That $16,000 is not subject to self employment tax and will be taxed at your marginal income tax rate. At 15% that would be $2,400 of tax and at 25% that would be $4,000 of tax.
Trade-ins are subject to the like-king exchange rules, which means that no current gain or loss is reported in the year of sale. If you trade-in your vehicle, the use of the like kind exchange rule is required and not elective if the property qualifies. But here, you are leasing after you gave your owned vehicle as trade-in.
If it is a "true" lease and at the end of lease you will return the car to the leasing company then there is no exchange as you are not the owner for tax purposes. The lease payments are expensed as paid.If it is a "capital lease", meaning (in most cases) that at the end of the lease term you would own the vehicle after a ten percent or less buyout, then the transaction is considered a "sale" and is treated the same as a purchase of another vehicle and may qualify as an exchange.
Please consult your tax practitioner with the lease details so a correct determination can be made if the new lease may qualify as a purchase (capital lease) and allow for the gain to be deferred.
I hope this helps for determining the tax liability that may be incurred.