Leia, princess, fighter, rebel, leader, Senator and we learned all that in the first 15 minutes of A New Hope. Its been over 30 years since we have seen her and quite a bit in her life has changed. However its fair to assume that not much has changed about Leia’s overall personality, a little older and wiser maybe but just as take charge and confident.
What do we know?
Leia was a leader in the Rebellion and she is now a General for the Resistance . She leads the Resistance which we believe is a separate organization from the Republic. This would mean she is no longer a political leader but a military one so her change from the begining of ANH(Senator) to the RotJ(Fighting on the ground) is complete.
After the events of RotJ Leia had a choice, study with Luke to become a Jedi or continue her work with the Republic . She decided she’d do the most good with Republic and now with the Resistance.
“It was a great question, and one that we talked about quite a bit, even with Carrie [Fisher]: If there was another, why did she not take advantage of this natural Force strength that this character had? And one of the answers was that it was simply a choice that she made, that her decision to run the Rebellion — ultimately, this Resistance — and consider herself a general, as opposed to a Jedi, it was simply a choice she took. Not that there was any regret that she could have and didn’t, but clearly we’ve seen, and we do again, she’s still Force-strong, and it’s something that is an intrinsic piece of her character.”JJ Abrams (Source)
So she is Force sensitive however she is not a Jedi and limited skills with the Force.
What we suspect
As the Leader of the Resistance she is tasked with stopping the First Order’s rise to power in the Galaxy. She is responsible for sending Poe to Jakku which starts all of our cast on its journey. After the Attack on Maz’s castle Leia leads the Resistance to Takodana to save the rest of the heroes and brings Han Chewie and Finn to the Resistance base. She is also responsible for the Resistance’s secret weapon which they use during the final battle of the movie.
Based on where we meet Han and the fact that Han goes to Maz instead of Leia we can assume that they no longer have the relationship they had at the end of RotJ. Speculation has named Kylo Ren Han and Leia’s son and possibly Rey as their daughter, making Leia a mother of at least one child. Considering where meet Rey and Kylo’s allegiance one would assume the loss of their child(ren) caused their estrangement. However they quickly put aside whatever the negative past is to fight once again against the darkside and save Rey.
By the end of TFA Leia will have won a battle against The First Order and most likely lost Han forever. She will have found a new family member in Rey, whether it be a daughter, niece or just in the Force is yet to be determined.