It depends on the lease. Tenants should specify signage contingencies and rights, or the landlord might demand that the sign be removed or moved elsewhere.If the premises has a marquee out front, the tenant should negotiate the lease terms to display their business sign there, too. When there's no marquee out front, tenants might request that they be allowed to get one installed. The landlord could agree to that, but it must be in the lease to ensure that things are done correctly.