Sci Fi series with slight Star Wars feel; female freighter captain from interstellar family business; monks with Jedi-like abilities. Several novels in series; read them in late 90s, don't think they were new at the time.
Sounds like the Mageworlds series, co-written by Debra Doyle and James D. Macdonald (a married couple).
I've only read Book 1. Back in the late 1990s, a paperback novel caught my eye as I was browsing in a store. It was the first of a series, and I remember that some of the sequels were already in print (I could see them right there on the shelf), but I don't believe I ever bought and read any of the later volumes. Major plot elements were much as you describe. It was, as you say, obviously going for a Star Wars-style feel. Does this cover look familiar?
The Price of the Stars was the first part of what was originally presented as a trilogy. It was published in 1992, and ISFDB says six more volumes in the Mageworlds series followed it, mostly released during the 1990s, with the last volume published in 2002. (Some of those later volumes were prequels.) So you, like I, must have run across it after most of the series was already in print. I've linked the title of Book 1 to its Amazon listing. It's available in Kindle if you want to refresh your memory. (Or you could order a paperback copy.)
I will describe some of the plot elements to show how well they match with your recollection.
The main protagonist in this first volume, depicted on the cover (the eyepatch is merely part of a disguise), is Beka Rosselin-Metadi. She is the daughter of Perada Rosselin, who, as a young princess, fell in love with (and eventually married) Jos Metadi, a General who was formerly a notorious privateer (I'm not sure if he was also a smuggler), back when they were working side by side, decades ago, during a big war to prevent the supernaturally-empowered "Mages" from conquering the rest of the Galaxy. The good guys won, thanks in no small part to the assistance of the much more ethical supernaturally-empowered "Adepts."
Anyway, all that is part of the backstory that's mentioned throughout the first book. A few decades after the end of the war, the daughter of Han and Leia -- excuse me, a slip of the tongue! Of course I meant to say "the daughter of Perada and Jos" -- is Beka, who trained to be a pilot and very much wants to follow in her father's footsteps by flying around the Galaxy as captain of her own ship and having adventures. As I recall, she absolutely does not want to inherit her mother's job as the hereditary monarch of their home planet, which would mean spending all day playing politics and signing documents while other people got to have all the fun. As the story begins, Beka learns that her mother has been assassinated, and Beka's father offers to let her take command of his famous ship, the Warhammer, if she will change her name and work undercover to investigate certain leads regarding who was really behind the assassination. (I don't think it will come as a huge shock when I tell you that those nasty Mages just might be involved.)
In the course of her adventures, Beka is joined by a mysterious old man who encourages people to simply call him "the Professor." He is more dangerous than he looks. It is hinted, and eventually established, that he is a surviving member of the Adepts, and thus is opposed to the Mages and all their works.
In other words, it's blatantly obvious that this storyline was heavily inspired by the original Star Wars trilogy (the first three films were all that existed when the co-authors started working on this series). I'm pretty sure that this is the same thing you were remembering.