Stewart started his role on 16 December after Rangers went six months without a chief executive following the departure of James Bisgrove to Saudi Arabia, while chairman John Bennett also had to step down in September for health reasons.
New chairman Fraser Thornton also began his role last month after a period of uncertainty in the Rangers boardroom, which Clement has had to contend with.
Rangers sacked Giovanni van Bronckhorst and Michael Beale in the last two campaigns after poor starts to the league but Stewart, who was interim CEO at Manchester United, says he and the club need grapple with wider issues.
Rangers reported a £17m loss last year but Stewart insists keeping faith with Clement is not a “financially driven decision”.
He confirmed a “root-and-branch review of the entire football department” will begin on Monday and says he met with Clement on Friday night to discuss results on the pitch.
“I can’t give Philippe any cast iron guarantees,” Stewart said. “He and I have both been around football long enough to know that isn’t the case.
“Equally, I’m not going to get into how many games does Philippe have to save his job, that’s not what we’re about.
“We’re about helping Philippe to identify why is there the inconsistency, and let’s address that.”
