The 32-year-old fell short in the 2016 Drivers' Championship to Mercedes team-mate Nico Rosberg but will not have the German to worry about in 2017 after his shock retirement back in December.
Hamilton will be joined by Valtteri Bottas in the Silver Arrows' livery this season and the Finn has insisted he will not let the three-time world champion have it all his own way.
However, the 1996 world champion, Hill, believes his fellow Brit will feel he has something to prove in 2017 and expects him to "re-double his efforts".
"Lewis was probably annoyed he did not win it last year," he said. "That was one that got away and I am sure he wants to put that right.
"Nico stopped because of the pressure of competing. He had his guts turned inside out to win the championship last year and there are only so many seasons you can do that.
"If Lewis goes away, lets off steam and does whatever he has to do to keep himself fresh then possibly that is a good thing. Lewis is a fearsome competitor and I think he will re-double his efforts after last year."