Yes, for the inca trail a permit is required and are sold out until september of this year. The alternative trails are salkantay trek 4d/3n or 5d/4n, lares 4d/3n, huchuy qosqo 3d/2n, moonstone trail, choquequiraw trek, huaracondo trek and the inca jungle trail. You can book these a week in advance.
