Conte was dismissed just four weeks before the start of the season despite winning the Premier League in his debut campaign and the FA Cup last season.
Thibaut Courtois moved to European champions Real Madrid on Wednesday for a reported 38million pounds (48.5million dollars, 42million euros).
Richarlison struck twice on debut for 10-man Everton to show he may justify his 50 million euros price tag and hold highly-fancied Wolves 2-2 on their return to the top flight.
Chelsea opened their Premier League campaign with victory against Huddersfield, while Tottenham, Bournemouth, Crystal Palace and Watford also made winning starts.
A frantic 48 hours in the transfer market provided Chelsea with a timely lift after last weekend's Community Shield defeat to Manchester City.
Liverpool weren't just the biggest spenders, but got their business done early and improved the key areas of Jurgen Klopp's squad that needed strengthening.
Thibaut Courtois has joined Real Madrid for a reported fee of $40.6 million on a six-year deal.
Chelsea agreed to sell Belgian goalkeeper Thibaut Courtois to Real Madrid in a deal worth around 35 million euros.
The 23-year-old is expected to replace Thibaut Courtois at Stamford Bridge.
Real will pay 35 million euros to bring the Belgium international, voted the best goalkeeper at the World Cup, to the Bernabeu, according to Marca.
Courtois, 26, has a year remaining on his contract and has been repeatedly linked with a move to Real Madrid
Gonzalo Higuain had been heavily linked to Chelsea before joining AC Milan from Juventus.
The last side to win the Community Shield and then go on to clinch the Premier League title were Manchester United in 2010-11.
The 26-year-old former Atletico Madrid number one has a year remaining on his Chelsea contract, but agent Christophe Henrotay said Courtois wants a move to the Spanish capital to be close to his two children.
Sunday's Community Shield is set to feature various youngsters and fringe players as FIFA World Cup 2018 stars ease their way back into club action.
Courtois' future at Stamford Bridge remains uncertain, but Sarri hopes the Belgium goalkeeper will stay.
Pedro has so far played in 131 games for the Blues, scoring 28 goals.
Bayern have just returned from a two-match tour of the USA, losing 2-0 to Juventus and 3-2 to Manchester City without Lewandowski and their international stars, who were rested after the World Cup.