According to the former presidential aide, the Obama administration did not pay much attention to Russia, considering the country as a regional power.
"But the world has changed completely. Biden can’t do Obama 2.0. They are going to have to think differently," Hill said on Tuesday.
Though the politician said that Russia posed "an insidious hybrid threat" to the United States, she noted that President Vladimir Putin's message to Biden was not hostile and expressed confidence that the two countries would be able to contribute to solving many urgent issues of international agenda despite their differences.
While the Obama administration was engaged with Russia on such issues as conflict settlement in Syria and Ukraine, Biden and Putin will have to cooperate on solving rather different problems, such as the climate crisis and the coronavirus pandemic, that gained new urgency over the past four years.
"I think over time, Russia is going to have to change the way they do things not because of our pressure but the sheer weight of the shifts in climate change," Hill said.
The politician added that the thawing polar ice cap had already led to competition for Arctic shipping routes near Alaska, which was never the case before.
"There has got to be fresh thinking on these issues," Hill said.
On Tuesday, Hill said at an online conference on US Agency for International Development operations in Eastern Europe that Washington should work with Moscow to stabilize bilateral relations in numerous areas while continuing efforts to repel the latter's clandestine subversive activities.