If I add a file to the same directory opened in NERDTree, the only way I can see the file added is if I quit vim and start it again .
Is there a way I can
As @romainl answered above; press r to refresh current directory or R to refresh root directory.
You can consider adding new files from nerdTree itself by pressing m, then a to add a new file (or directory by adding a trailing slash). This way you don't need to refresh nerdTree to see the new added file.