Chiefs were riding high when current Bafana Bafana coach Stuart Baxter delivered the league and MTN8 double in 2014/15, having claimed league and Nedbank Cup honours two seasons prior.
However, three barren years followed under the tutelage of Steve Komphela, who resigned in April after fans went on the rampage in the wake of a Nedbank Cup semi-final loss to Free State Stars at Moses Mabhida Stadium.
Zulu, who was signed at the beginning of last season from Maritzburg United, says his side have to bring the glory days back to Naturena.
"We have to step up. Three seasons with the team not winning anything is unheard of," says Zulu, who played in 28 league matches in 2017/18.
"It is imperative that we win something as we are a revered club and known also as a big team.
"We have to bring back those glory days and win, and make sure that our fans are happy again. Because they are the ones who are behind the team.
"We play for them in making sure that they remain happy."
Chiefs will start the new campaign against Nedbank Cup champions Ea Lla Koto in the MTN8 quarter-finals in August.