As Leia did not discover that she was a child of a Jedi until ROTJ, she would not have been able to intentionally use it. She also did not have any training so her use of the Force would be limited compared to other people who had been trained and studied it for years.
Abrams says Princess Leia chose not to train in the ways of the Force. In the films, while Luke trains to become a powerful Jedi, Princess Leia is kept busy by essential duties of her own. Later, as the leader of the Resistance, General Organa has her hands full with tasks that don't involve any use of the Force.
The reason Darth Vader could sense Obi-Wan and Luke was because of how they actively used the Force several times throughout the Original Trilogy. Vader never sensed Leia because she didn't the Force; Leia did not even know she had Force powers to begin with.
Now that she knew the truth about her parentage and her Force powers, Leia trained as a Jedi with Luke, honing her Force abilities and constructing a lightsaber. But she ended her apprenticeship after having a vision that her Jedi path would end with the death of her son.
You see Leia use the force in several instances. When Luke reached out to her on Bespin, she felt him in the force and guided Lando to him. Even as late as episode 7, you see Leia's reaction when she felt Han die. While Leia never trained as a Jedi, new canon/as far as we know, she is most definitely a force user.
Leia Organa-Skywalker
Leia is shown to be Force-sensitive. In The Empire Strikes Back, Leia professes her love for Han Solo when he is put into carbonite stasis, although it is originally Han and Luke who compete for her affections.
Masters. For other uses, see Finn (disambiguation). Finn, formerly designated FN-2187 ("Eight-Seven"), was a Force-sensitive human male stormtrooper who served the First Order until his desertion and subsequent defection to the Resistance during the First Order-Resistance War.
He was thinking to himself how he could not wait to train Leia, as she had all the qualities of a good Jedi, unlike Luke. However, after Obi-Wan died on the Death Star, his spirit went to Degobah, where he convinced Yoda that training Luke was the better option, saying that Leia wasn't ready yet, but Luke was.
Encased in a distinctive silver-and-copper hilt, Leia's lightsaber used a naturally-occurring blue kyber crystal, much like Luke's original saber that he had inherited from his father by way of Obi-Wan Kenobi.
While training under Saba Sebatyne, Leia's lightsabers were taken by her new Jedi Master, who told her that they did not reflect her skills anymore, and that it was time that she build a new lightsaber, one fit for a fully-fledged Jedi Knight.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence. "Sister," the Emperor taunted.
However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover she was his daughter. That serves to justify Vader's lack of awareness of his connection to Leia, although, perhaps, not as satisfyingly as if Lucas had planned for the relationship from the beginning.
Padme didn't have any force powers and she was too old to become a Jedi. She may have had some kind of force powers whilst pregnant with Luke and Leia but being with Anakin could have caused some force sensitivity at the time.
Leia's journey yields a time dilation of 62.6 days; however Luke experiences a time dilation of 700.8 days (1.92 years). The students concluded that Luke is therefore 1.75 years younger than Leia, possibly rendering them the first twins ever to have over a year between their ages.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.
A crystal embodies the Jedi as the heart of the lightsaber, and pure kyber has no color until it's bonded to the Force user. This process likely resulted in Rey Skywalker's lightsaber being yellow.
This can be seen in the novel starwars.wikia.com/wiki/Rogue_Planet. It's because of his mastery of sorsue (sorry for my bad spelling.) Well if you want the ACTUAL reason it because in the original 3 films the Green Light Sabre didn't exist until after Obi Wans death.
It's possible that Rey adopted the yellow-bladed lightsaber (or perhaps the kyber crystal conjured a yellow blade based on the changes within its wielder) in honor of those emotionally detached sentinels tasked with guarding the Jedi Order.
As Chewbacca's long-time friend, Leia most likely would have been aware of this custom and wanted to respect his traditions. Due to this, Leia found Rey, who had looked up to Han as a father figure, and hugged her instead. Later, Star Wars: The Force Awakens showed Chewbacca mourning alone.
Carrie Fisher's Leia Organa Solo was intended to be the actual last Jedi in Disney's Star Wars saga, according to the late actor's brother Todd Fisher. "She was going to be the big payoff in the final film," Fisher told Yahoo. "She was going to be the last Jedi, so to speak.
This upcoming new Star Wars book reveals that Yoda always thought Leia was the more powerful force user in the Skywalker family. And that she was the true chosen one who would bring balance to the force.
There is another instance after that moment where Poe (Oscar Isaac) nags Finn to reveal the truth about what he wanted to tell Rey, but Finn never budges. All signs pointed to Finn telling Rey he loved her, but fans were left confused why Abrams didn't answer such a major question.
By the end of The Rise of Skywalker, Rey had become the last known Jedi of the Skywalker Saga. With all that being said, Rey was not left as the last remaining Force-sensitive character.
Then, we have reports that at a fan Q and A session, director JJ Abrams supposedly said that what Finn was going to tell Rey was that he was Force sensitive, something we see demonstrated in the film pretty clearly in a number of different moments.