Payet signed a new long-term contract with West Ham earlier this week which will keep him at the Boleyn Ground until the summer of 2021.
“I just hope now that he performs,” former West Ham striker Hartson told talkSPORT about Payet. “He doesn’t just play for next seven or eight months, and then his performances start to wear off.
“I hope he goes and treats his new contract as a big plus for him and as a huge sign of West Ham going places under Bilic.”
Payet joined the Hammers from French club Marseille in the summer of 2015 and has been truly superb so far this campaign.
The attacking midfielder has a pass accuracy of 82% and a shot accuracy of 72%, and has won two headers, 47 dribbles and 12 tackles.
West Ham are seventh in the Premier League table at the moment with 40 points from 26 matches.
For the Hammers to rise up the league table, Payet will have to maintain his form for the rest of the season.