The first Test between India and Australia is scheduled to begin at the Adelaide Oval on December 17.
The inclusion of Zampa, alongside Chahal and all-rounders Moeen Ali, Washington Sundar among others makes them a better spin unit.
Zampa joins the likes of Yuzvendra Chahal, Washington Sundar, Moeen Ali and Pawan Negi, strengthening the team's spin attack.
Richardson has so far played 14 games in his IPL career so far and has picked up 18 wickets. The bowler played for Pune Warriors India in 2013, Rajasthan Royals in 2014, and RCB in 2016.
The ICC, on Wednesday, said it will wait for another month before taking a call on the T20 World Cup, scheduled to be held in Australia in October-November.
The pacer had informed the team's medical staff on Thursday night of the complaint and was tested for COVID-19.
The pacer informed the team's medical staff Thursday night of the complaint and has been tested for COVID-19, with the results still pending.