Stewart began his role on December 16 after Rangers had been without a chief executive for six months following the departure of James Bisgrove to Saudi Arabia, with chairman John Bennett also having to step down in September for health reasons.
New chairman Fraser Thornton also started his job last month after a period of uncertainty within the Rangers board that Clement had to deal with.
Rangers sacked Giovanni van Bronckhorst and Michael Beale in the last two seasons after poor starts in the league, but Stewart, who was interim chief executive of Manchester United, insists he and the club must deal with wider issues.
Rangers made a £17m loss last year, but Stewart insists keeping faith with Clement is not a “financial decision”.
He confirmed that a “bottom-up review of the entire football department” would begin on Monday and claimed he met with Clement on Friday evening to discuss the on-field results.
“I can’t give Philippe any ironclad guarantees,” Stewart said. “We’ve both been in football long enough to know that’s not the case.
“I’m also not going to go into the number of games in which Philippe has to save his job because that’s not what we want.
“We want to help Philippe identify the cause of this inconsistency and address it.”
