If the container sits on private property, such as your driveway or inside a fenced job site, Benton does not require a placement permit. That covers most residential rentals in town.
It changes once any part of the container reaches a city street or right-of-way. Benton publishes no standalone dumpster permit. Work that occupies a street is handled as a street cut, and the city routes it to one office.
That office is Community Development at Benton City Hall, 410 River Street. The street department's own answer sends residents there for a street cut permit, and the department takes calls at 501-776-5938, Monday through Friday from 7 a.m. to 6 p.m. The same office issues demolition, grading and utility construction permits, so if your project needs one of those, you can sort both out in one call.
No fee is posted for this permit, and no review time is posted either. Ask when you call, and build a few days into your schedule so approval lands before the truck does. If you are not sure whether your drop spot counts as right-of-way, your account manager can get you to the right person at the city.
Before you book, confirm with the city that a container can be placed for your job at your address. Rules differ from city to city and they change. Your Prime Dumpster account manager will help you check, and will tell you plainly what your options are here.