Mr Hanson was elected as Opposition Leader on Monday following the resignation of Zed Seselja.
The new leader was warned almost immediately by both the Greens and Labor leaders that he will need to change his attitude.
Chief Minister Katy Gallagher says Mr Hanson's ego is an issue.
"He's been the bully boy of the Liberal Party. That's the role he's played," she said.
Greens MLA Shane Rattenbury says he hopes Mr Hanson will offer more ideas than criticism.
"Jeremy Hanson has a very aggressive style of politics. Certainly in the chamber he plays it extremely hard," he said.
"He seems to have no boundaries when it comes to his conduct in the chamber and there'll be a challenge for him as leader now to step up and improve his contribution to the assembly and to ACT politics."
Mr Hanson says he will not seek to redefine the party's leadership, but rather be his own man and let others judge him for that.
He says he is disappointed that some people describe him as a bully.
Mr Hanson says he has always tried to be respectful when holding Labor to account on difficult issues, but he does expect to change his style now that he is leader.
"Well I probably will just because it's a different job. But I know I've got a big job in front of me. That there's a lot of experience that I need to get under my belt. And I intend to do that," he said.
"I imagine that as I grow in the job that the way that my persona develops will change as well but there's no deliberate intent to do that. You just see that with leaders that they tend to grow into the job."
Ms Gallagher has also criticised the party for allowing Mr Seselja to continue being paid as an MLA while campaigning for a Senate position.
Mr Hanson has indicate he will allow Mr Seselja to remain on the party's front-bench until later in the year.
Ms Gallagher says that is not appropriate.
"He's got a very healthy salary here but I don't think taxpayers should be paying for his Senate campaign and Mr Hanson should require that of him as a new leader."
Today's first Legislative Assembly sitting for 2013 will be the first opportunity to see the performance of the Opposition's new leadership team.
Much of the first sitting week will be devoted to the scrutiny of annual reports for 2012.
Also tabled will be half-yearly reports on budget performance by government directorates.
Environment Minister Simon Corbell will present the latest report card on how Canberra is faring in the the achievement of the Government's ambitious greenhouse gas reduction targets.
Some bills will also be debated, including proposed legislation to change how betting agencies pay fees to racing clubs.