Her father is both a noble and a senator
could be a senator from within the subsector, either a world with senators or the subsector itself has a senate.
Simplest interpretation is a Government: 4 world where her father has achieve Social: B (and is therefore of "noble" status).
If you want to take this from a chargen perspective, what happens to people on the Noble career track? (LBB S4)
Well, first you have to succeed at a Position roll.
Success then gets you "assigned and posted" as in Imperial Noble to an appropriate world somewhere, representing the Emperor.
Then you roll for Promotion, which if successful raises your Social Standing, but the odds of success are low.
In other words, most Knights (Soc: B) remain Knights. Promotion to a higher Social rank is RARE (and will usually mean being reassigned to a new world into the bargain!).
Well, at some point, even Nobles will either fail their re-enlist roll or otherwise choose to retire and "muster out" of service in the Noble career chargen path. At that point, they retain their Social Status as nobles, but they are no longer "in post" as a representative of the Emperor to a world.
So what do "retired nobles" DO with themselves after they retire (if they don't become PC Travellers)?
Well ...
If they are well liked and popular with the citizens of a world, it's entirely possible for a (now former) Imperial Noble to make the jump into (local) world politics and win an election to a world's planetary senate (Government: 4 Representative Democracy) to continue a lifetime of public service, but now with a new constituency (emperor vs popular vote).
That is the SIMPLEST way to "square the circle" involved in that rumor from LBB A1 The Kinunir.
Of course, the OTHER simplest way to "square the circle" involved in that rumor is to realize that the young lady involved is
LYING to the PCs and the whole story/rumor that she's telling them is completely made up!
Remember, not every rumor has to be 100% true ...
... some of them could be false ...