It's not a plot hole, because it has nothing to do with the plot. It's just missing information. Nearly every question anyone has about this movie is due to cut content and deleted scenes. The film should probably have been about 20 minutes longer and been allowed to breathe and build the world more.
The Resistance is a militarized force that actively combats and harasses the First Order. The Republic is the official new government of the worlds that rebelled against the Empire, and officially they disavow the Resistance because they are in an unsteady truce with what remains of the Empire. (The First Order is NOT the Empire, it's basically a cult that sprang up within the remnants of the Empire...another thing the movie doesn't make clear.) There is a deleted scene with the woman the movie seems to expect us to know when the Hosnian system is destroyed, in which we learn she is Leia's liason to the Republic, and Leia goes into how much the Republic hates her for refusing to cease hostilities against the Empire. Leia implies that if she went to the Republic capital herself, she would be quietly assassinated.
It's clear that Lucasfilm was terrified of talking for one second about the politics or governmental situation of the galaxy in TFA, and that left a lot of unanswered questions floating around. You can thank the people who whined and screamed about "OMG POLITIX BORING" regarding the prequels for that.