You should consult an attorney about the actual meaning of this lease clause and appropriate methods to enforce your rights as a landlord. Under no circumstances should you try to use self help to remove a commercial tenant (or purported "licensee") until you have consulted with an attorney. You run the risk of becoming liable for treble damages for conducting an illegal eviction.
The above constitutes general information only and should not be considered legal advice.
Dear Flushing Landlord:
You likely did not draft this "License" agreement on your own, so you and your attorney must have devoted time to determining whether this clause could allow for self-help in event of a breach of lease and cancellation for a default in paying rent. The usual rule of thumb in New York, especially in NYC, is that commercial occupants in breach of the obligation to pay rent, must be sued in the NYC Civil Court, Commercial Landlord and Tenant Part, for nonpayment of rent by means of a summary nonpayment proceeding.
A commercial lease or a license containing a conditional limitation clause purporting to allow the landlord to exercise self help is likely not enforceable. If the tenant visits an attorney, the threat to terminate the license based on a default in paying rent, may allow the tenant to gain a Yellowstone Injunction, and if so obtained, tie up the landlord in a litigation in Queens County Supreme Court for a long time.
Consult with an attorney. Even if your interpretation is legitimate and correct, it is not likely a lawyer would recommend self-help over the usual route of a nonpayment proceeding. If the advice is wrong, or correct, but a court and a jury disagree and decide that the tenant was damaged as a result of an unlawful eviction, the monetary judgment the tenant gains could be significant and cost you title to the property.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
"Self-help" is not favored by the courts. In fact, it can get you into a lot of trouble. I'd recommend that you find a good commercial attorney, or one who practices landlord-tenant law. Because of the way that license agreement was drafted, with what to me are many unenforceable provisions, you really need a lawyer.
I am an attorney admitted solely in NY. None of the answers I submit on this forum constitutes legal advice, even to questioners in NY, and no attorney-client relationship is hereby created.