There are multiple ways to cancel a trademark and subsequently, there are multiple options to exercise once a trademark has been cancelled:

• If a trademark is cancelled because an owner failed to submit scheduled maintenance documentation and accompanying fees for an existing mark, the owner may not later request that the mark is reinstated. The owner must file a new trademark application. 
• If a trademark owner can prove that a trademark cancellation is the result of an error on the part of the Trademark Office, the owner can ask to have a mark reinstated or file a petition with the Director of the Trademark Office.  Such an error would include failure on the part of the USPTO to make appropriate changes after receiving written notice of an address change.
• If a trademark cancellation is the result of a third party petition to cancel an existing registration of a mark, the trademark owner can contest the petition and request that the mark is reinstated. 
• If a trademark owner submits the appropriate documentation and a trademark is cancelled because such documentation is not received in the Trademark Office, the owner can ask to have the trademark reinstated if the owner is able to provide proof that the documentation was sent and the error lies either with the letter courier or the USPTO.