Injuries and the form of Seamus Coleman has limited Hibbert to just 10 appearances since the start of the 2012-13 campaign.
However, having committed his future to Everton by signing a new two-year contract extension last night, the 33-year-old is hoping that the club's involvement in the Europa League could open up more opportunities for him to feature.
"I picked up a few injuries [last season] but I'm fit and I'm ready to go," the defender told the club's official website.
"Because of the amount of games that we are playing and the way the manager likes to keep people fresh, he might introduce players who haven't played the week before. The games will come thick and fast, so it is very important to have a good, strong squad."
Hibbert has spent his entire career with the Toffees, having made his debut in 2001.