Bale's world-record move to Real Madrid – for a reported fee of €100 million from Tottenham – was finally completed on Sunday.
The 24-year-old has battled a foot injury in recent months and is short on match fitness, making him no guarantee to start Real's next match, against Villarreal, on September 14.
And Clement has warned Bale that he needs to work hard, and be flexible, if he wants to become a modern-day club legend.
"There's a lot of competition for places. No-one will be guaranteed anything," Clement told BBC Sport.
"Coach Carlo Ancelotti has a clear idea how to use him but things can change. At Southampton, Bale played at left-back which he also did at Spurs where he became a more left-sided player.
"He recently became more central. He's got that versatility. Carlo is flexible enough to use Gareth and other players in different capacities."
While Bale's attacking prowess is undoubted – he scored 26 goals in 44 appearances for Tottenham last season – he will not be the club's sole outlet, like he often was at White Hart Lane.
The likes of Cristiano Ronaldo, Karim Benzema and Isco are all available to manager Ancelotti and Clement said Bale will not be rushed in for the Villarreal match if he is not fit.
"Gareth has the goalscoring talent and ability to set up goals for others," he said.
"We have a lot of exciting players here (though). (Striker Karim) Benzema is a great talent, while Isco plays in midfield but has chipped in with three goals already.
"Depending on how much or little he plays will depend whether he trains a week on Wednesday or Thursday leading into the first game at Villarreal."
Former Brazil international Ronaldo also warned Bale that he must make an early impression at the club, believing that the Welshman's pricetag will be held against him.
"It is only normal that, whenever he puts in a poor performance, the fans will remind him that the club paid €100m for him," Ronaldo told Radio Barcelona.
"I can only recommend to Bale that he does not let his price tag become an obsession."
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