This largely depends on the make and model, but for most SUVs and trucks, you will need a lift kit to fit 35-inch tires. You could put 33-inch tires on most off-road-focused SUVs without any lift kit, but for 35-inch tires, it is a must.
A lift kit essentially raises the vehicle's body or suspension to create additional space for larger tires. This modification not only prevents interference with various mechanical components but also can improve the vehicle's ground clearance, which can be beneficial for off-road applications. Moreover, it will stop the tires from rubbing against the fender or wheel wells.
However, a lift kit changes the geometry of your suspension, which puts more strain on the components. Also, it significantly affects the center of gravity, handling, and overall dynamics of the vehicle, making it less stable overall.
For that reason, I would only recommend installing lift kits from reputable manufacturers, which were tested before they hit the market. Some kits that I tried in the past are near dangerous and unsafe. In addition, I would highly recommend going to a professional shop for the installation, as a poorly installed kit can significantly compromise your vehicle's safety.