The advice came today from Hearts legend Gary Mackay, who fears the big Lithuanian defender will give boss Ally McCoist a "heart attack" if he doesn't change his ways.
Zaliukas joined the Gers on a free transfer this summer after leaving English Championship club Leeds United.
He has performed well in pre-season matches and is expected to start alongside Lee McCulloch in the SPFL Championship this season.
Mackay, though, believes the 30-year-old centre-half has to cut out the "moments of slackness" that were a regular feature of his seven-year spell at Tynecastle.
Instead, Zaliukas must take the safety-first approach that won Weir, another ex-Jambo, so much silverware at Ibrox.
Mackay said: "Marius is a good defender, but he will occasionally take a chance.
"Knowing Ally McCoist and Kenny McDowall, they will make it clear to him straight away that is not the right thing to do at Rangers.
"Whether it is at Ibrox or away from home, sometimes the right thing to do is simply hit the ball into Row Z.
"One of the best defenders I ever played alongside was Davie Weir. He was just so effective. He knew when to play and when not to. Zaliukas has to pick up on on that. Every four to six weeks at Hearts Marius was prone to giving the manager a mild heart attack. The likes of Weir would never do that.
"It is just part of Marius's make-up. When he is on top of his game he's a very dominant centre half. When he isn't on top of his game, however, he can let a bit of slackness creep into his play.
"When a top player like Davie or Sandy Jardine wasn't on top of their game they'd make sure they didn't make any daft mistakes.
"Zaliukas should try to do that because he will not get away with it at Rangers in the way he perhaps did at other clubs in the past."
Despite holding the Hearts appearances record after 640 games between 1980 and 1997 Mackay acknowledges that Zaliukas will have to adapt to the sheer size of the Ibrox club
He said: "My old managers Alex MacDonald and Sandy Jardine always used to tell us Hearts are a big club in Scottish terms but Rangers are on another level.
"There are parallels to be made between the way the supporters of both clubs have stood by them during difficult times in recent years.
"For Rangers to get 45,000 fans at games in the third and fourth tiers of Scottish football was incredible.
"But this season there will be a different atmosphere at Rangers games. They will be expected to deliver. Zaliukas did that very well at Hearts, where he won the Scottish Cup in 2012. But he is going to have to do it week in, week out at Rangers.
"Marius will realise that from the first moment he represents Rangers in a competitive match."
Mackay, a Fifa-registered agent, represents Rangers and Scotland left-back Lee Wallace.
The pacy defender has already welcomed the arrival of his former Hearts teammate at Ibrox and spoke of their "telepathic" link.
Mackay feels Zaliukas will enjoy the presence of Wallace alongside him in the Gers back line. He said: "Lee and Marius will benefit from that knowledge and understanding they both have of each other's games from their time at Hearts.
"Having Lee there at a club of the size and stature of Rangers can only help Marius both on and off the park."
THE spine of the Rangers team in the coming season will have a strong Hearts connection, with Zaliukas, Wallace, Ian Black and David Templeton all having played for the capital club.
All four played together many times for the Maroons.
Mackay feels that link could be helpful to the Light Blues' chances of winning a third consecutive promotion and completing "The Journey" back to the top flight.
He said: "Ian, Lee, Marius and David all took different routes to Hearts, but they were all very successful there. That has stood them in good stead over their careers.
"Over the years there have always been strong links and a lot of mutual respect between the two clubs.
"I played at Hearts with ex-Gers like Derek Ferguson and Dave McPherson and was also managed by Sandy Jardine and Alex MacDonald.
"I am looking forward to seeing the two teams play in the Championship.
"Rangers against Hearts is one of Scottish football's great fixtures. The games between them should be fascinating."