Ms Rudd was appointed on Friday after Esther McVey’s resignation on Thursday over Theresa May’s draft Brexit deal with the EU.
Steve Webb, director of policy at Royal London, said: “In a large and complex department like the DWP, there is a risk that the attention of a new Secretary of State is quickly focussed on complex and contentious issues like sorting out Universal Credit.
“But pension policy is also of vital importance to millions and we urgently need a Secretary of State who gives it the attention that it deserves.
“A particular priority should be to drive forward the Pensions Dashboard, as well as making sure that there is a Pensions Bill in the next Queen’s Speech.
“That Bill should make it compulsory for pension schemes and providers to send data to a dashboard, as without compulsion the project will fail.
“Legislation could also be used to improve automatic enrolment, implementing previously agreed improvements such as bringing in younger workers.
“And DWP should tackle other unfairnesses such as the way in which some low-paid workers do not get tax relief on their pension contributions and the way that thousands of mothers are missing out on credits towards their state pension.
“There is much to be done in the pensions space and I hope that Amber Rudd will be make time to focus on the changes that are needed.”
Tom Selby, senior analyst at AJ Bell, added: “Right now domestic pensions policy issues are probably a long way from Amber Rudd’s mind as Westminster lurches from on Brexit crisis to another.
“However, once the dust has settled she will find a department facing challenges on a number of fronts.
“For Rudd it is very much a case of out of the frying pan and into the fire.
“Having left the Home Office – a department still dealing with the fallout from the Windrush scandal – Rudd will now have to defend the Government’s Universal Credit programme and its treatment of WASPI women facing hikes in their state pension age.
“If she stays in the job long enough she could be required to shepherd through an acceleration in the state pension age increase to 67 and 68, hardly a popular policy.
“The recent slowdown in life expectancy improvements may yet demand a review of the plans, although it remains unclear whether this is a blip or a longer term trend.
“More immediately, Rudd will have to decide whether the Pensions Dashboard project – which was reviewed and eventually backed to a degree by her predecessor – should go ahead as planned. Automatic enrolment is also reaching a crucial phase, with contributions set to rise to 8% of earnings from April next year.
“All of this may seem unimportant given the nation’s current obsession with Brexit, but they are hugely important and affect the lives of millions of people in the UK.”
Jon Greer, head of retirement policy at Quilter questioned whether Ms Rudd would remain in post long enough to get to grips with her new brief.
He said“Is six the lucky number for the Department and Work and Pensions?
“One would hope so since Amber Rudd has become the sixth Work and Pensions Secretary since March 2016 when Iain Duncan Smith left the role after six years.
“However, the chances of Rudd being the concrete force able to weather the political storm is unlikely.
“Her fate is tied to that of the Prime Minister who is undeniably on shaky ground.
“In fact that alliance is probably one of the main reasons May added her back into the Cabinet, as Rudd’s experience with pensions seems a bit sparse.
“While political shifts aren’t unusual in all aspects of Government the impact is particularly poignant in the DWP, which is responsible for long-term savings policy.
“How can the public be confident in consistent policy around pensions and long-term savings if the DWP leadership changes almost as often as the calendar year?
“However, it’s encouraging to note that Rudd has already proclaimed her support for the Pension Dashboard.
“And if she’s looking for an easy win before year-end then she should provide clarity on the Government’s role in the dashboard and ensure her department publishes its feasibility study swiftly.”