The Aboriginal community is looking to new Premier Peter Gutwein for land returns while unions want him to tackle low wages and rising living costs.
Aboriginal Land Council of Tasmania chair Michael Mansell said he would write to Mr Gutwein seeking a meeting to try to "mend" what he called a fractured relationship between Aboriginal people and the government.
"We want to discuss land returns and put protection of our Aboriginal heritage and Aboriginal tourism back on the agenda," Mr Mansell said.
"If you want to make your mark as premier, and leave a legacy, you need a good relationship with Aboriginal people.
"A lot of Aboriginal people know him personally from when when he was just the publican at Bridport. He treated people fairly and we hope that translates into his new job as premier"
Mr Mansell said former Liberal Premier Ray Groom, the first to return land to Aborigines, and Labor Premiers Paul Lennon and the late Jim Bacon had supported Aboriginal people.
"We will ask Premier Gutwein to build a relationship with Aboriginal people based on respect and dignity," he said.
Unions Tasmania secretary Jessica Munday said Mr Gutwein would need to work hard to "win over" working Tasmanians.
"Upon election to government, Mr Gutwein sacked nearly 1,000 public sector workers, attempted to freeze their wages and override the Tasmanian Industrial Commission," Ms Munday said.
"More recently, he teamed up with Will Hodgman to deliver further damaging cuts of $450 million that an already struggling public sector cannot afford and doesn't deserve."
The big issues facing Tasmanian workers such as low wages, casualisation of jobs and high youth unemployment were a priority, Ms Munday said.
Tasmanian Chamber of Commerce and Industry chief executive Michael Bailey welcomed stability with the new Premier "who has done an excellent job as Treasurer for the past six years".
"Mr Gutwein and Deputy Premier Jeremy Rockliff represent a stable platform from which the government can continue for the next two years before the next election," Mr Bailey said.
"I have great confidence that his Government will continue to grow the Tasmanian economy for all Tasmanians.
"The State will again have a Northern Premier, who understands what is needed for half the State and its population."
Mr Bailey paid tribute to Infrastructure Michael Ferguson and said his withdrawal from the leadership contest "was the best result for the entire State".
Launceston Chamber of Commerce executive officer Neil Grose says business "takes great confidence" from Mr Gutwein's election.
"The economic gains of the past six years have been achieved by strong leadership in partnership with a capable team implementing the right business-orientated policies and the Chamber looks forward to Mr Gutwein continuing that good work,' Mr Grose said.
"It is now very important that Mr Gutwein announces the new cabinet make-up with minimal delay and disruption so that business can get on with the job of growing Tasmania's economy."
Tasmanian doctors want health to remain a priority.
Australian Medical Association Tasmanian president Professor John Burgess said he was looking forward to a productive relationship with the government.
"AMA Tasmania stands ready to provide advice and support to achieve the best health outcomes for all Tasmanians," Professor Burgess said.
"As a group, we recognise this as a possibility to reset the agenda, a greenfield opportunity if you will."
TasCOSS chief Kym Goodes said she hoped Mr Gutwein showed compassion and empathy to address the challenges facing Tasmanians.
"We know what matters most to Tasmanians is the government's ability to deliver the most basic essential services for all Tasmanians," Ms Goodes said.
"As the divide between Tasmanians living in poverty and the broader population continues to grow, the enduring legacy of the Gutwein Government must be prioritising investment to tackle entrenched social disadvantage."
The RACT is hopeful Mr Gutwein will focus on road safety and tackling congestion.
RACT spokeswoman, Stacey Pennicott said Mr Gutwein was well placed to tackle Tasmania's mobility challenges.
"As Treasurer since the Liberals came to power in 2014, Mr Gutwein has overseen funding boosts for road upgrades across the state," she said.
The Northern Tasmania Development Corporation has congratulated Peter Gutwein on his elevation to Premier today.
Northern Tasmanian Development Corporation chief executive Mark Baker said Mr Gutwein had had a long and successful career in both politics and the private sector.
"As Treasurer, Mr Gutwein has been a major player in the economic success of Tasmania," Mr Baker said.
As the first Northern Tasmanian premier for several years, Mr Gutwein will bring a keen understanding of issues impacting the region, he said.
"More importantly, he will be supported by cabinet ministers who are also well versed in the opportunities ahead of Northern Tasmania."
Launceston Mayor, Albert van Zetten wished Mr Gutwein all the best as leader.
"As a Northern Tasmanian it's of course pleasing to see someone from our region serving as premier," Councillor van Zetten said.
"I look forward to continuing our work with the State government on initiatives like the Launceston City Deal, aimed at making Launceston one of the great regional cities of the world."
Burnie mayor and former Labor deputy premier Steve Kons said it was "fantastic" that Mr Gutwein was the new premier.
"I've not seen anyone better for the job," Councillor Kons said. "He's a good operator."
Councillor Kons said it would make no difference having a Northern premier.
"You still have the same bureaucracy so it won't make any difference," he said.
Master Builders Association Tasmanian executive director Matthew Pollock said Mr Gutwein had always looked after small and medium businesses.
"We look forward to working with Premier Gutwein and his leadership team so that (the) building and construction industry in Tasmania remains the strongest in the country, and to ensure we have the workers with the right skills to deliver the record pipeline of projects ahead of us," Mr Pollock said.
National retailers also hailed Mr Gutwein's elevation to the top job.
Australian Retailers Association executive director Russell Zimmerman, said Tasmania's retail sector had been a key driver of Tasmania's expanding economy.
"The ARA would like to offer its heartiest congratulations to Premier-elect Gutwein on being elected by his colleagues to lead Tasmania, and the ARA looks forward to working with him as Premier to continue the good work that's been done in partnership with the government in the retail sector," Mr Zimmerman said.