It is possible that she was the inspiration for the Rebellion's decision to wear a proper holster with an actual gun in Return of the Jedi. As a child, she saw a different kind of battle on the ground, something she decided to take on as she led the fight against the Empire and the First Order.
A decade after the events of Star Wars: Episode III - Revenge of the Sith, Obi-Wan Kenobi sees the Jedi Master keeping a low profile in Tatooine. She lost her credibility after it was revealed that she was the daughter of Darth Vader. The revelation of Obi-Wan's secret history with young Leia is one of the most surprising aspects of the Obi-Wan show.
As the Empire closed in on the small proto-Rebel cell, Tala sacrificed herself to ensure the safety of the other refugees. The Disney+ series tackles Obi-Wan's dark days after the fall of the Galactic Republic and the rise of the Empire. At the end of the Obi-Wan Kenobi finale, Leia has a holster that she wears. His boring life takes an unexpected turn when he is asked by the Inquisitor the Third Sister, Reva, to rescue the kidnapped Leia, a secret ploy by the Inquisitor the Third Sister, Jimmy Smits.
After founding and leading the Star Wars Resistance, she transitioned back to being a boots-on-the-ground type of leader as General Organa. During Obi-Wan's run, the pair develops a strong bond as the Jedi tries to bring the Princess home. She can see firsthand how dire the situation is for normal people and Force-sensitive people under the Empire's rule. This is the only time she wore a holster throughout the Star Wars original trilogy. She was eager to participate in the Rebellion despite the danger, even in her early teens.
Despite not being in the original trilogy, Leia's holster in Obi-Wan is important to her overall Star Wars arcs. In the brief time they spend together, they start to look up to each other for being brave and doing the right thing.
After Obi-Wan Kenobi, there hasn't been any mention of Tala's holster.
Along their dangerous journey, Obi-Wan and Leia meet various new characters and some of them end up being devoted allies, including Tala. She transitioned from her political career to that of the Rebellion's founder.
It's safe to assume that her experience in Obi-Wan will last a long time. The character wasn't mentioned in either of the original or sequel trilogies. She transitioned to a different cause as the fight against Emperor Palpatine became more intense. Outside of a visual connection to her later belt and blaster, the holster seems inconsequential at this point. Her holster serves as a reminder to her that there are other ways to change than being a politician.
The first season of Obi-Wan Kenobi can be watched on Disney+.