Yes. Your exam is valid for a period of two years. Under normal circumstances, in order to have you become licensed or registered, your sponsoring firm would have filed Form U-4 (in addition to meeting other requirements such as bonding, fee payment, and a background check).
However, since your employment was terminated prior to this point, you have two years to become employed by a member firm and become licensed. After this point, you may have to rewrite the exam. However, some jurisdictions have the discretion to waive an individual's requirement to rewrite after an exam has expired. This usually happens when the person in question has continued to work within the financial industry, but in a position that didn't require licensing. For more information, contact your State Regulator. A directory of State Regulators is listed here
When you passed your Series 7 examination, the Central Registration Depository (CRD) permanently recorded your score. Therefore, your new employer will be able to verify that you successfully completed the exam and the licensing procedure can begin.
To read more about the Series 7, see Solving Mixed Options Problems On The Series 7