The works are in preference to alternatives such as relocating the highway, building a higher bridge or building a debris basin, which the agency considers to be "excessively expensive".
Concurrent applications have been made to the Queenstown Lakes District Council and the Otago Regional Council.
The application also seeks consent to deposit about 120,000 cubic metres of debris in a cleanfill site on land belonging to Lonestar Mt Albert Station, next to the Makarora River.
About 30,000 cubic metres of cleanfill has already been deposited there from previous floods.
Pipson Creek floods have closed State Highway 6 eight times since 1998, with massive boulders and large quantities of silt inundating the bridge and spilling on to neighbouring land.
NZTA says it has incurred significant costs from emergency works to repair the damage.
A report by Associate Prof Tim Davies, of Canterbury University, identified options for relocating the highway, building a higher bridge or building a debris basin, but these were "excessively expensive"and unlikely to happen soon, the application said.
But NZTA also felt doing nothing or the minimum was unacceptable.
Even though no other cleanfill site other than Mt Albert Station had been considered, it was the best site because it was close, which would minimise truck movements and be economic, the application stated.
The station owners have approved the application.
Prof Davies has estimated a debris basin should be able to contain between 100,000 cubic metres and one million cubic metres of debris.
It could be built north of the present channel on a slope leading down to Millionaires Flat, or at the fan head upstream of the bridge, requiring a very deep structure.
While a debris basin would protect the highway and the township of Makarora, the costs would be "excessively expensive compared to regular maintenance and emergency debris removal as and when required", the NZTA application states.
Engineers have estimated there is capacity for 15,000 cubic metres of debris to come down in a single flood event.
The debris flows are caused by intense rainfalls in the head of the catchment.
