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 .
NERDTree
Is there a way I can
Personally I prefer to trigger the refresh automatically when focusing the NERDTree window. This autocommand (in your .vimrc) will do it
.vimrc
autocmd BufEnter NERD_tree_* | execute 'normal R'