Frances has branded Morag "a worthy and antagonistic character." She also describes her as an "independent, amazingly strong woman, but I think she now realises family is what matters most, and she'd probably like to stay in the Bay." Holy Soap said Morag is known for her "barbed comments and cold, cruel demeanour". Morag has softened over time around certain characters but Frances said "she still holds her own, and she's still this very strong independent person." Frances believes that Morag should never find happiness with a lover because "she's put so much doom on everybody". A lot of things have happened to her, that are ultimately her own fault. Frances added: "So it's that nemesis that keeps coming back for the things she has done to other people". Morag's main connection in the serial has been with her brother Alf Stewart. There has been a lots of fights and antagonsim between the pair. Morag later softens towards him. Frances said: "She's been through so many mishaps with, underneath she will always care for him and look after him." She holds a great deal of "love and concern" for him which Morag is "reluctant to show a lot of the time". Frances felt it perhaps not the best development because she enjoyed their "wonderful fights".
Morag grew up in the bay and was close to brother, Alf. It is learned before her appearance that Morag is a magistrate. Her niece, Roo contacts her to do a background check on Alf's new fiancee Ailsa Hogan which reveals Ailsa had severed time in prison for murdering her abusive father. In June 1988, Morag returns to Summer Bay to attend Roo's wedding to Frank Morgan and soon learns that Roo is pregnant and Frank is not the father. She advises her to come clean to Frank about the baby's paternity and Ruth does so on the day of the wedding. After Roo becomes a pariah, Morag lets her stay with her in the city but this does not last when Roo learns Morag is conspiring with Brett Macklin to get Roo to sign over custody of their unborn child to him.
Morag reappears for the funeral of her nephew, Alan Fisher and later enjoys sparring with Colleen Smart, a former schoolmate who constantly gets on her nerves. Shortly after she return to the city. It is later revealed that Morag had a secret child with Donald and then put the child up for adoption. Her daughter is then revealed to be Bobby. She is angry to find out Donald is her father, she is even more angry when she finds out Morag is her mother. Morag and Bobby never got on. Morag is later involved in a plane crash at sea. Morag survives but is in a coma. Bobby decides to wait until she wakes up to tell her how much she hates her. Following the collapse of her marriage to Richard, Morag settles in the bay permanently. Danny Farnsworth takes a job working for Morag as her assistant under an assumed name but he has an ulterior motive; to gain revenge of her for sentencing his father to prison, resulting in his suicide. Danny begins playing mind-games with Morag and when she exposes him, he loses control and tries to kill her but Donald and Bobby are able to calm Danny down. After this, Morag returns to the city and puts her house on the Market. When Bobby dies in a boating accident 1993, Morag returns and tries to gain custody of Bobby's adoptive son Sam Marshall. When Ailsa finds out about her plans she manages to stop her.
In 2001, Morag decides to come back to Summer Bay to see her family. She is now a judge and she presides over the trial of Kane for his sexual assault of Dani. She returns in 2002, this time staying longer. She comes and goes again. During her stay, Morag found herself set against Angie Russell. Their many battles nearly resulted in Morag getting sued after accusing Angie of attempted murder. Morag also attended to Alf's health after he insisted Ailsa was back from the dead. While trying to get Alf medical attention, Morag nearly died after he pushed her down the stairs. Fortunately, Alf got the help he needed and a brain tumor was removed in surgery. Morag later decides to move back into the town forever and the following year she faces Dani in court once more when she is on trial for running over Kane and sentences her to imprisonment after Dani is found guilty. After that, Morag was involved in a series of scandals. In 2005 she decides to help the locals over power Project 56. Josh West becomes the mayor and along with Amanda Vale's help, they try to enforce the project. Along the way, Josh frames Alf for money embezzlement, seeing Alf sent to jail. Morag then declared a battle on Project 56. However, Morag's interference in Josh's plots nearly cost Morag her life. After deciding to back off, Josh is then shot dead. Morag finds out her friend Barry Hyde is Josh's murderer and questions him with Peter Baker (Nicholas Bishop) listening in. After Peter arrested Barry, Morag then felt sorry for him and defended Barry in court, gaining him bail.
Barry's son Kim is later wrongfully accused of sexual assault and Morag is first on the scene to defend him. She also defends Robbie Hunter over allegations he killed his grandfather. Then she helps Brad Armstrong on his drug and assault charges after he is framed by Johnny Cooper. Morag also becomes suspicious of Martha's new boyfriend Ash Nader and tries linking him to Johnny's gang. In 2007, Morag learnt that Ash was married and attempted exposing the truth. Ash told Martha himself but managed to convince her to stay with him. After Morag managed to set everyone in town against Ash, Martha accused Morag of giving Bobby up for own selfish reasons and for not being able to understand love. Hurt, then returns to the city to work as a magistrate, wanting to redefine herself in her work. She later returns to help her great-nephew Ric Dalby when he is charged with the murder of Rocco Cooper (Ian Meadows). She then exposes Jazz Curtis after she lies about her mother's death and inheritance.
In 2008, Morag was involved in several scandals. Morag is horrified to learn that Colleen is actually her half-sister. She starts being mean to Colleen for interfering in Stewart family business. They argue on different occasions, until Morag goes to far. She later makes up with Colleen and lets her have a role in their life. She later befriends Aden, she becomes determined to help him with his issues. Over time the pair bond and she is only one who can make him see any sense. He confides to her about all the abuse of his childhood, she then looks out for him whenever he gets into any trouble. Morag also managed to save Miles Copeland from losing his teaching position after a disturbed parent attempted to frame him for child abuse. She then solves Sam Holden's murder. She then sees an old friend, police officer Ross Buckton, who is planning on retiring. She starts a relationship with him and they eventually marry. He is then diagnosed with Alzheimer's disease, she leaves with Ross so he can receive the correct treatment in the city. She comes back to support Martha after her husband Jack Holden (Paul O'Brien) is murdered. She then exposes Bridget Simmons's lies, then leaves again.
She returns in 2011 for Ross's funeral and to support Alf after he is accused of Penn Graham's murder. She tries to expose Will Smith as the killer, but her interference results in Will escaping town and later getting arrested. Alf's name is later cleared. She then meddles with Nicole's plans to give her baby away, she has a go at her and reminds her that she gave her own child up. Morag then finds out about Elijah and Grace Johnson's sham marriage, she agrees to keep quiet and helps Grace. Morag realises that Charlie Buckton is dating Darryl Braxton and manages to stop Charlie from revealing the relationship to her friends and family. Once Alf returns from his trip away, Morag takes a job in the city. She briefly returns to the Bay for Charlie's funeral and takes Ruby Buckton home with her. Morag becomes concerned that Ruby has not grieved for Charlie properly and encourages her to return to the Bay. Sid Walker contacts Morag and brings her back to Summer Bay to help defend his daughter Sasha Bezmel when she is accused of the murder of her ex-boyfriend Stu Henderson. Morag defends Sasha in court and she is found not guilty. Morag later helps Ruby, when a bag of marijuana is found in her bag at the airport. Morag returns for Roo's wedding to Harvey Ryan. Following the wedding, Morag stays for a few days but Alf gets fed up of her and Colleen's presence and tells them to leave.