Malcolm Turnbull said after ousting Tony Abbott in a leadership coup he believed the Parliament would serve its full term, but what would that term look like under his leadership?

1. When will we go back to the polls?

Mr Turnbull told reporters last night that it was his "assumption" that the Parliament would serve its full term.

The next scheduled election is about a year away, but there are double dissolution triggers already on the shelf if the predilection is to go early.

This result of this weekend's by-election in the West Australian seat of Canning is likely to have an influence on what happens next.

2. Climate policy & same-sex marriage

Mr Turnbull's personal support for same-sex marriage and previous push for an emissions trading scheme put him at odds with Mr Abbott and many conservative colleagues.

The Prime Minister-designate's office said he would hold the line on both fronts with the existing position as prosecuted by Mr Abbott. That would mean a plebiscite on same-sex marriage.

Mr Turnbull has also said the climate targets that have already been announced — under Mr Abbott — ahead of the Paris meeting are expected to continue.

3. Indigenous affairs

Mr Abbott made a controversial decision to move Indigenous Affairs into the Department of Prime Minister and Cabinet.

He also oversaw the formation of an Indigenous Advisory Council to consult on Indigenous policy and a restructure of the way money was spent in the portfolio.

Further to that, Mr Abbott wanted to see a referendum held to recognise Indigenous Australians in the constitution, and while he has said it should not be rushed, he did endorse May 2017 for the vote. The new leader's approach is unclear.

Malcolm Turnbull's approach to Indigenous affairs is unclear. ( AAP: Paul Miller )

4. Bringing together the 'broad church'

One of the big criticisms of the Abbott government was that too much was micro-managed out of the Prime Minister's office and there was not enough collegiate decision-making or freedom for ministers to prosecute their portfolios.

Mr Turnbull has pledged to bring together the many strands of the Liberal Party in "a culture of engagement, of consultation, of collaboration".

Mr Turnbull and Deputy Leader Julie Bishop are considered 'small l' liberals and the far right of the party is likely to be alienated by some more moderate policy approaches.

The Nationals are also threatening to make life difficult, and to bargain hard with Mr Turnbull for a new Coalition agreement.

Malcolm Turnbull and Julie Bishop are considered 'small l' liberals. ( AAP: Sam Mooy )

5. Can he change his approach to those who defy him?

Mr Turnbull has a reputation for having a fiery temper and for not being afraid of delivering a severe dressing down when he's not happy with someone's performance.

Will he be able to rein in his emotions and bring together an inclusive Cabinet-style government as promised?

Many who have known him well, and his style in Opposition, have labelled him presidential in his approach.

Mr Turnbull was sending an inclusive message last night: "The prime minister of Australia is not a president."

"The prime minister is the first among equals and you can see the partnership between me and Julie, the partnership with our colleagues will be a very clear cultural demonstration that we are operating in a traditional Cabinet manner," he said.