Emergency services have not ruled out the possibility of the cyclone ratcheting up to a Category 5 system as the cyclone intensifies in the Gulf of Carpentaria.
But the threat is not over for communities near Tennant Creek, 500km inland, as the Bureau of Meteorology on Sunday warned of heavy rain and destructive winds in the NT's east.
"I'm concerned that people haven't spent the time doing precautions they should; putting cyclone screens on houses, tie down caravans and trailers and outdoor furniture, anything that can become a missile".
"If you're in Trevor's path you've made all the necessary preparations and now is the time to stay safe and remain in shelter", a Bureau of Meteorology spokesman said in a video update. "Very soon the winds will rapidly increase from the opposite direction to just as fast or even stronger than before".
Meteorologist Todd Smith warned the cyclone, which is now moving southwest at 16km/h, could change direction or surge to category five as it intensifies.
The last category four tropical cyclone to hit the WA coast was Christine in December 2013.
The eye of the cyclone is estimated between 30-50km wide.
Australian iron ore supply shouldn't be too disrupted by Cyclone Veronica, unless it floods the mines
Iron ore operations in Australia's Pilbara region are unlikely to be impacted significantly by Tropical Cyclone Veronica, unless it leads to flooding at mines, says Vivek Dhar, Mining and Energy Commodities Strategist at the Commonwealth Bank.
"Currently near the centre we're looking at mean winds of a hundred kilometres per hour but gusts up to 140 kilometres per hour", he said.The cyclone should track south to southwest today before taking a more south to southeast track on Saturday and impact the coast.
Red Cross emergency services spokesperson Paul Mitchell said Red Cross has an excellent free resource available to help people prepare for an emergency.
The centre of the storm is now located around 95 kilometres west of Port Hedland.
Trevor left behind a trail of damage in Queensland's Cape York Peninsula earlier this week, uprooting trees, causing flooding and roof damage, closing schools and roads, and knocking out power supplies.
Meanwhile in the west, the category 4 system of Cyclone Veronica was nearing Port Hedland late on Saturday night.
Residents are being told the cyclone could sweep through at about noon.More news: Barça confirm Messi injury and he won＇t play against Morocco