The 33-year-old has made over 300 appearances for the club since his debut in 2000, but has been used as a back-up for Seamus Coleman during much of Martinez's tenure.
With Coleman's attacking intent earning him the plaudits at Goodison Park, Hibbert has had to wait until recently to regain his place under Martinez - with the Irishman suffering from a hamstring injury.
Hibbert has started against Swansea City, Liverpool, Krasnodar and Manchester United in recent weeks and is getting used to the attacking duties Martinez asks of his full-backs.
"I think the system he plays means he's happy for us to go forward and get involved more but we've also still got to keep a defensive mind in that when we do attack," Hibbert told the club's official website.
"We've got to keep our shape and be covering ourselves defensively.
"It's difficult [getting up and down] – you've got to be fit to do it but you can pick and choose your times to get forward.
"But the system also means that if we do get caught out going forward, there may be one or two midfielders that can help out behind you.
"That's the modern age now and the full-backs have to get forward as much as possible."
Coleman has not featured since mid-September, but could be available for selection shortly after the international break.
