Is there some kind of trigger or event in Vim that is fired whenever a Vim command is executed?
Eg. say I execute tabnext or NERDTree is there some function which can be setup to listen for required events and perform some action when it detects that those events?
Vim has something called "autocommands" (:help autocmd-intro). These allow you to execute arbitrary code upon events like saving a file or changing to a different window.
Unfortunately, to my knowledge, there's no autocommand that is executed for any command. It might be possible to do something different, though:
cnoremap <silent> <cr> <cr>:call <SID>CommandCallback()<cr>
function! s:CommandCallback()
let last_command = @:
if last_command =~ 'tabnew'
echomsg "Tabnew was called"
endif
endfunction
This code overrides the <cr> key ("carriage return", the "enter" key) in command-line mode to press <cr> and then call the function s:CommandCallback. You can check the last command in the command-line history with the @: magic variable, or by using histget (:help histget()). You can then inspect the command and do whatever you like with it.
EDIT: Some elaboration on "do whatever you like with it"
If you want some status message visible in the statusline, you could set a global variable with the value, something like let g:command_message = 'Tabnew was called'. Then, you can render it in your statusline with %{g:command_message}. You'll need to read :help statusline to learn how to fit it in your particular statusline, but it shouldn't be difficult.
Opening it in a separate window would be more tricky, because you'd need to open a scratch buffer with particular settings, check if one already exists, and so on. It's perfectly doable, but a pretty long topic. I've got a plugin that might help, but not sure if it would be appropriate for this: https://github.com/AndrewRadev/bufferize.vim. You could also check out this plugin: https://github.com/mtth/scratch.vim. You'll need to experiment, see if any one of these can fit your use case, or you could poke around in their source code, and try to learn how to manage the window yourself (it would be a useful skill to have, so I'd definitely recommend it :)).
s:CommandCallback function is script-local, so it needs to be called from the same script. You can read more about this with :help s:. You don't need to, of course, you can define the function with function! CommandCallback() and call it with :call CommandCallback, but then it'll be defined globally.echomsg output to a different window, or a different status line, something which will always be visible, perhaps located in some set area of the screen independent of which tabs or windows are active?