By the end of The Last Jedi, Rey has stolen Luke's Jedi texts from Ahch-To. Clearly, she is set to begin her quest towards mastering the ways of the Jedi.
Taking over the mantle as the last Jedi from Luke will be daunting for her, but she will surely have some help from Force Ghost Luke and possibly Yoda as well. Therefore, we could be set to see her training a new group of young Padawans, like Luke during flashbacks of his time training Ben Solo.
However, for Rey to assume the rank of Jedi Master and train the next generation of Jedi, we may need the movie to skip over a few years in a similar way to Return of the Jedi and Empire Strikes Back.
This seems unlikely as Rey becoming a Jedi Master is a crucial part of the characters' development, and it would be a waste for us to miss her biggest achievement since becoming a Jedi. It is more likely we will see Rey achieve the rank of Jedi Master, and should she survive to the end of the movie, go on to train others in the Jedi way.
Either way, expect at least one appearance from Force Ghost Luke in Episode IX.