NEWLY elected Solomon MHR Natasha Griggs has threatened to cross the floor and vote against her party on issues that may hurt the Territory - such as the nuclear waste dump.

Ms Griggs' vote could prove crucial in the new parliament, which is expected to have either a Labor or Coalition minority government.

Her predecessor - Labor's Damian Hale - voted against the nuclear waste dump, but was overruled by his party. But the tight numbers in the new House of Representatives could give Ms Griggs the power to block such legislation.

"I've always said that the Territory is my home and that I will fight for issues for the Territory," she said.

"If there are individual issues that arise that I need to cross the floor (I will)," Ms Griggs said.

She said she wouldn't do it on every issue but only on those issues where there was need.

She said she would do it for particular issues that were important to the Northern Territory.

Ms Griggs said she would remain with the Coalition and only vote against her own party if the Territory was getting a "raw deal".