Wright's Outback Wrangler TV show co-star Chris "Willow" Wilson was hanging from a sling under the chopper on a mission to collect crocodile eggs when he died in the February 2022 incident.
Wright was charged after being accused of tampering with evidence to cover up non-adherence to aircraft maintenance rules.
Wright last week pleaded not guilty to three counts of attempting to pervert the course of justice.
The start of the trial has been delayed several times due to legal argument and scheduling issues.
However, a jury is scheduled to be chosen on Tuesday for the trial before Acting Justice Allan Blow in Darwin's Supreme Court.
The trial is expected to take up to four weeks and hear from about 25 witnesses.
An Australian Transport Safety Bureau report into the crash near the King River in Arnhem Land found the chopper's engine stopped mid-flight because of a lack of fuel.
The crash into a paperbark swamp killed Mr Wilson, 34, and critically injured pilot Sebastian Robinson, 28.
The charge of attempting to pervert the course of justice carries a maximum 15-year jail term in the NT.
Wright rose to fame starring in National Geographic's Outback Wrangler and Netflix series Wild Croc Territory.
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