Mantic Dorn
Old school...
This description is no longer valid diue to the Jedi Order, as a faction, having left the service of the Republic.
On the Jedi in the Republic

The mysterious jedi order and the Galactic Republic has shared a long history together.
Having Always been seperated bodies the two organisations has seen much together, in victory and defeat.
Up to this day the jedi of the order holds a protective hand over the Republic and in return the Republic offers the jedi reasources, equipment and space ships the order could not muster on itself.
Foremost the two work together in order to surpass the darkness and evil of the galaxy in where one can not ignore the other if light and order shall rise voctorious.
The Jedi Order is a sub organisation within and outside of the Galactic Republic. While its core has a solid place in the Republic not all members of the jedi order considers the Republic worthy of their support, much as not all within the Republic considers the jedi as trusted allies.
The Jedi order is a minor faction that openly supports the Galactic Republic.
The jedi are not officials in the Galactic Republic but can be asked to advice on political matters by the senate, the Galactic Republic head of state or other instance of the Republic government.
The Jedi Order does not automatically hold a rank within the Republic armed forces but can be asked to advice on military matters by the Republic Military on any level. A request for jedi assistance in military actions is considered a normal procedure when Republic armed forces enters a conflict but there is nothing forcing individual jedi of the order to take part in it.
The Jedi knights of the Jedi Order answers to the Grand Master of the jedi order.
The Galactic Republic head of state and the Grand Master have means to be put in direct Contact with each other at all times.