In Infinity War, it is briefly mentioned that Thanos
went to Xandar, destroyed half the population and took the Power Stone.
the Nova Corps
still exist? If so, in what capacity?
I am going to do my best to properly cover up spoilers but if you have not seen Infinity War and you don't want anything ruiined, STOP READING NOW
The Actual Answer
We don't know. It has not been addressed in any canon fashion yet.
According to the MCU Wiki they were
the intergalactic military and police force of the Nova Empire
AND we know they operate at least one off world installation
These two points suggest that at least some of them were
not on Xandar when Thanos attacked.
At this point, it bears mentioning that
when he got his hands on all 6 Infinity Stones, Thanos was able to kill off half the life in the Universe at random. Prior to this, the exterminated half of the population of any planet he attacked would heavily favor the local military, police forces and anyone else who tried to stop the coming genocide-the rest would come from those rounded up after the fighting was over.
every member of the Nova Corps present on Xandar at the time of the attack fought Thanos and they fought to the last and did not surrender
The worst case scenario is that
every member of the Nova Corps stationed on Xandar is dead but those off world could still be alive and operating in some reduced capacity.