It depends on what kind of civilisation you are writing about.
What I mean is, if your writing is exploring or representing aspects of human nature/politics/scientific curiosity/ etc. in a galaxy spanning civilisation, then said civilisation needs no other fundamental reason for the study of a star other than "Because it's there." Otherwise why would mountain climbers keep trying to summit Everest, countries argue over who "owns" the Arctic circle, or, to a certain extent, scientists bother with repeating experiments? Or even why would anyone watch paint dry (just to see how boring it is!)?
So this immediately offers some solutions: for sport, due to a border dispute, to confirm previous findings, or even just to explore the use of a turn of phrase. It may even be for religious reasons similar to Sybok's search for Sha Ka Ree. Or, to repeat, merely because it is there.
Is it as a result of scientific endeavour:
Is it a naturally/artificially formed star? If artificially, perhaps it is merely being monitored or perhaps it is malfunctioning.
Is the star already exhibiting interesting behaviour (a type of radiation we've never encountered before, John) and further study is required?
In addition, is it a remote-probe or a manned-probe?
If the former, perhaps it is a test of a newly developed material/scanning system/method of transmission? If the latter, has this been done before/is it dangerous/is it a school field trip or experiment?
Is it down to galactic resources:
Is the star a potential power source for a transportation device? Or a weapon? (though perhaps not a good choice given a recent Lucasfilm/Disney production)
Is the star being surveyed for a potential mining opportunity?
Does your galaxy spanning civilisation need to make sense, for the reader, of why it is sending a probe at all? For example, any of the alien items encountered by the protagonists of H. P. Lovecraft stories (admittedly they usually do just make the person go mad but that's not usually using the item for it's intended purpose!), or even more simply "Everybody has a Plumbus, but how are they made?..."
There is also the possibility that the civilisation has reached such an advanced point in technological achievement that the inhabitants now know only THAT they live in this galactic community and THAT this machine allows faster-than-light travel etc. but they no longer remember how or why. An extreme example of this would be the film Idiocracy.
Consequently, even though the civilisation may be technologically advanced, the collective knowledge base is relatively limited, so even a launching a simple solar probe would not be considered a redundant action.
I hope this helps/I haven't overlapped too much with other's answers!