It might sound quite surprising to you, but our Sun is itself a dwarf star ( A yellow dwarf star, to be precise). Spoiled your curiosity? Sorry! The term "dwarf star" was coined to distinguish main-sequence stars in terms of their luminosity, mass, and size (for sure).
Red dwarfs are smaller than our Sun and they consume less hydrogen (which is fuel for stars) in their core, thus their surface is cooler than that of the Sun. And that's the exact reason why they are red. They are the slowest among all their fellow sequence stars and therefore, live longer than our Sun. They are the most abundant type of stars that you can find in galaxies. Why? Because they require less matter to form.
Now coming to our original question, what if we somehow kick the Sun out of our Solar System ( you need a golf stick of 31 million km) and put a red dwarf in its place?
The first thing you will notice on Earth is that the Sun (now a red dwarf) is no longer brighter than it used to be. Trust me! It would be very dark as the luminosity of red dwarf ranges between about 0.0001 and 0.1 times that of the Sun. So be ready for perpetual darkness and never-ending cold nights.
Secondly, it will start getting very cold on Earth. Why? Because the location of the Goldilocks' Zone would be changed. It would be very close to the Red Dwarf. Even Mercury would be too cold to create an ideal temperature that is needed to support life. So you need to readjust the location of the Earth too if you don't want to die from hypothermia. Also, there
Generally, the mass of a red dwarf ranges from 0.075 to about 0.50 solar masses and has a surface temperature of less than 4,000 K. So, its gravitational pull would not be enough to hold our solar system anymore. Many planets (especially outer gaseous planets ) may escape out into the deep interstellar space or else, they may crash into each other. So you should be prepared for another mass extinction!
Even if you did readjust its location, there is a high probability of tidal locking implying that one side of Earth would permanently face the star and the other face would be always turned away thus creating extreme temperature difference.
There can be a solution for that too. Intense cloud formation on the star-facing side of a tidally locked planet may reduce overall thermal flux and drastically reduce equilibrium temperature differences between the two sides of the planet.
Well, not to disappoint you, there is a very high chance that everyone dies but if you play your cards wisely, you might survive. Many dwarf stars in our galaxy are said to host 10 billion planets (Super-Earths) that are present in the habitable zone. So, Don't give up on your quest of finding aliens in them! Other than that, there is a benefit of having a red dwarf as your sun. Due to its longevity, you need not worry about the star's death because they are S-l-o-w.
At last, we can say that there is still hope for the survival of the new red-dwarf star.