Q:

How to bring back NERDTree tab if I accidentally closed it? 

I have a NERDTree setup nicely on my Rails project:

Sometimes, when I do fuzzy finding (Ctrl + P), I would accidentally still be on left tab; when I went to the file, it would replace the nerdtree's left tab.  See screenshot below:

Super simple question, but how can I bring up the Nerdtree display back up like the first screnshot? 

A:

You should just be able to run :NERDTree again. 
Additionally, I have this setting in my .vimrc, to make it less likely I'll delete the NERDTree buffer by accident with I'm compulsively typing :bd
autocmd FileType nerdtree cnoreabbrev <buffer> bd :echo "No you don't"<cr>

Deleting the buffer will permanently put NERDTree in hell (Vim plugins are usually brittle).  If you do that, you have to restart Vim. 
Also, if you use tabs in Vim, you should get NERDTreeTabs (dead but it works) which keeps NERDTree open / closed / in the same state across all tabs you have open, which is a standard design practice in all editors except Vim.  I have a mapping set up to toggle NERDTree:
nnoremap <Leader>nt :NERDTreeTabsToggle<cr>

steal from my my vimrc!