It's darn likely that you will need another appraisal. If I'm wrong then you reap a benefit to save some money. Good luck.
If you have done an appraisal with the mortgage company and have not yet been approved by a bank...I am not happy with that. Appraisers are being assigned to the banks...you should not have an appraisal until you have a pre-approval (pre-commitment) from a certain bank. Mortgage brokers cannot pick an appraiser and have it done (to the best of my knowledge).
Please call your attorney and discuss this....or give me a call and we can talk about the details 631-425-6150 Gail Gladstone