The Foxes boss snapped up the 28-year-old midfielder in a £12million deal from Spanish side Sevilla in the summer transfer window, but the player's hopes of making an early name for himself in the Premier League were thwarted by a groin injury suffered in pre-season.
Iborra played in the entire 90 minutes of the Carabao Cup win over Liverpool last month and finally made his Foxes Premier League bow in the goalless draw against Bournemouth ahead of the international break.
And Shakespeare is now keen for him to start showing what he is capable of when the action resumes against West Brom at the King Pwer Stadium on Monday.
"It is important he kicks on from here," he told the Mercury.
"He has had a stop-start season because of his injury and he is now becoming fully fit. He is vastly experienced and he will use all that experience going forward."
"His English is getting better but he uses football language in terms of pointing and he knows the players’ names now," added Shakespeare.
"You can see that from just half-a-game his experience. After all those years at Sevilla, he knows the game.
"It is pleasing to get him out on the pitch because he has had a stop-start first part of the season.
"He is unflappable. I spoke about his credentials early on about him being a real team player. You are not the captain of Sevilla without reason."