The definite answer to your question is no.

At least I don't know how to do it globally in Django, whereas global includes middleware exceptions).

Further, as request by @Shubham Kumar, the hook you need is process_exception and for an implementation check this SO post with the offical docs on how to activate it. As stated in the Django docs:

request is an HttpRequest object. exception is an Exception object raised by the view function.

Django calls process_exception() when a view raises an exception. process_exception() should return either None or an HttpResponse object. If it returns an HttpResponse object, the template response and response middleware will be applied and the resulting response returned to the browser. Otherwise, default exception handling kicks in.

Again, middleware are run in reverse order during the response phase, which includes process_exception. If an exception middleware returns a response, the process_exception methods of the middleware classes above that middleware won’t be called at all.

Meaning that you will merely be able to hook into the view function and catch all those exceptions.

Since I came across with a similar situation that lead me to this question, I'll answer following the original question that is related to Django Rest Framework specifically and not just Django.

I understand that you want to handle raised exceptions from your views, globally, without having to define try/except blocks on each view module.

DRF allows you to define your own Custom Exception Handling mechanism (docs). Here is an example:

At my_custom_except_handler.py:

import logging
from rest_framework.views import exception_handler
from django.http import JsonResponse
from requests import ConnectionError

def custom_exception_handler(exc, context):
    # Call REST framework's default exception handler first
    response = exception_handler(exc, context)

    # checks if the raised exception is of the type you want to handle
    if isinstance(exc, ConnectionError):
        # defines custom response data
        err_data = {'MSG_HEADER': 'some custom error messaging'}

        # logs detail data from the exception being handled
        logging.error(f"Original error detail and callstack: {exc}")
        # returns a JsonResponse
        return JsonResponse(err_data, safe=False, status=503)

    # returns response as handled normally by the framework
    return response

As stated in the docs, the defined response object refers to:

The exception handler function should either return a Response object, or return None if the exception cannot be handled. If the handler returns None then the exception will be re-raised and Django will return a standard HTTP 500 'server error' response.

In other words, 'response' won't be None only when handling these exceptions docs:

• Subclasses of APIException.
• Django's Http404 exception.
• Django's PermissionDenied exception.

If your custom handler returns None, then the exception will be handled 'normally' by the framework, returning typical 500 server error.

Finally remember to set the required key at settings.py:

REST_FRAMEWORK = {'EXCEPTION_HANDLER': 
    'my_project.my_app.my_custom_except_handler.custom_exception_handler'}

Hope it helps!