The defender has made only 10 senior appearances in all competitions over the last two seasons as he has battled a series of injuries while Seamus Coleman has established himself as first-choice right-back.
But the 33-year-old has committed his future to Everton for the next two seasons, and he hopes the extra fixtures generated by their qualification for the Europa League will enhance his chances of first-team action.
Hibbert also insists he is "fit and ready to go" following his various injury problems, and he is looking forward to the challenge of forcing his way back into Roberto Martinez's plans.
"I picked up a few injuries (last season) but I'm fit and I'm ready to go," Hibbert told evertontv.
"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."
Coleman was voted Everton player of the season, and Hibbert added: "Seamus has been unbelievable and deserves his place for the way he is playing.
"It's one of them where we need players in the squad that will keep fighting for each other and pushing each other for places."