Clement is the new Rangers manager and kicked off his reign by leading the Gers to a 4-0 win over Hibernian at Ibrox on Saturday.
The Belgian has been charged with reviving Rangers’ fortunes after the club fell well short of expectations under his predecessor Michael Beale.
With Rangers set to face Hearts in the Scottish League Cup semi-final next month, Clement has a big chance to win his first trophy at Ibrox even before Christmas.
However, Hartson insisted that Clement’s reign early at Rangers will still be judged on league form and whether they end up making progress in the Scottish Premiership moving forward.
He concedes though that winning the cup would give a boost to the new manager and the fans early in the Belgian’s reign.
Asked how winning the cup would affect Rangers this season, Hartson said on the Go Radio Football Show: “A lot will depend as well on how are they going in the league.
“They have got to keep progressing in the league and got to keep trying to challenge.
“If they win a cup that will give the club a big lift, it will obviously boost the supporters and it will show Philippe Clement that he can possibly win a cup.
“For me, he has got a very difficult job and I think everybody appreciates that.”
Clement’s winning start against Hibernian is sure to boost the feel-good factor at Ibrox, but next up for the Gers is a trip away from home comforts to meet Sparta Prague in the Europa League.
