The full-back has made just 10 competitive appearances for the Merseyside outfit since May 2012 due to a series of injuries.
Despite those woes, Hibbert penned a two-year extension at Goodison Park on Tuesday.
With Everton set to participate in the UEFA Europa League this season, the fit again 33-year-old is hoping to feature more prominently.
"I picked up a few injuries (last season) but I'm fit and I'm ready to go," Hibbert told Everton'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."
Seamus Coleman has been Everton's regular right-back for the majority of the two previous campaigns, and Hibbert believes the Republic of Ireland international is fully deserving of his place in the starting XI.
"Seamus has been unbelievable and deserves his place for the way he is playing," he added. "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.
"Every season you are a professional footballer you have got to be looking over your shoulder and seeing who is coming through to fight for your place. It's a natural instinct that comes with being a footballer."
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