Dunne impressed in his first outing for McLaren when he set a time just 0.069 seconds off Formula 1 title contender Piastri at the Red Bull Ring.
He described that has “the best day of his life”, and he will now get a second opportunity as McLaren take the second of four mandatory practice sessions for rookie drivers.
By driving in Italy, Dunne will have had two outings, while IndyCar star Pato O’Ward will drive at his home race in Mexico.
The location and driver at McLaren’s fourth rookie session of the year has yet to be confirmed, but with a number of street circuits and sprint weekends to close out the season, the final round of the season at Abu Dhabi appears to be a strong possibility.
With two victories, Dunne has shown impressive form for Rodin Motorsport in Formula 2 since his Austrian Grand Prix appearance but has dropped to fifth in the standings.
He finished second on the road in the feature race in Austria but was disqualified for excessive plank wear on his car, and he lost victory after dominating in the wet in Belgium because of a penalty for a start procedure infringement.
While both penalties were out of his control, it dropped the Irishman from first to fifth in the standings with four rounds left.
