Here, the PA news agency takes a look at what is in the in-tray of the new man at Selhurst Park.
Sort out contract situation
There are 12 first-team players out of contract and one of them, Andros Townsend, revealed in May the club were waiting to appoint a manager before deciding who would get new terms. While Christian Benteke signed a two-year deal in June, several key players remain free to leave including Joel Ward, Gary Cahill and Patrick Van Aanholt. It might suit Vieira to let a large amount of the squad depart in order to bring in his own players, but the experience of those who could exit is invaluable and some will surely remain.
Bring down average age
A challenge for chairman Steve Parish and sporting director Dougie Freedman in recent transfer windows has been to freshen up the playing group. Everyone at Selhurst Park has been more than aware for some time there is a need to bring down the average age of the squad with numerous players aged 30 or over. Some of the elder statesmen will exit on free transfers while the signings of Nathan Ferguson, Ebere Eze and Jean-Philippe Mateta - who are all 24 or below - during the last 12 months have helped, but Vieira will be involved in convincing more hungry, talented youngsters to join the Eagles.
Coping without Eze
Eze proved a huge hit with the Palace fans after a £20million transfer from QPR last summer. After contributing four goals and six assists during his debut campaign in the Premier League, even more was expected for this term but an Achilles injury in May looks likely to rule the playmaker out for the rest of 2021. Coping without arguably the club's second-best attacker is a big blow to former Arsenal captain Vieira and he will have to find a way to cover the loss of Eze's creativity.
Manage latest Zaha saga
As with every transfer window, the topic of Wilfried Zaha's future is back on the agenda. Hodgson was able to handle the speculation impressively and - aside from a modest 2019-20 season - ensured Zaha remained unaffected by the constant talk over a move. That job is now Vieira's and with Eze out for the foreseeable future, Palace's reliance on last season's top goalscorer feels greater than ever. A hefty bid could tempt Parish and Freedman to part ways with the Ivory Coast international if the funds can be reinvested in the squad, but the new boss would surely prefer to keep hold of the club's star player.