I'm developing a story where, in the near future, a long range telescope is sent out further in to space than ever before.
What would this telescope need to have in order to A) be a significant improvement to what we currently have and B) be able to see life on a distant planet?
A telescope's resolution is limited by its aperture for collecting EM radiation. Proposals for higher resolution telescopes in space involve placing multiple recievers in a fixed constellation, and using computer processing to combine the resulting images. This is called an astronomical interferometer.
A proposal to do this was the Terrestrial Planetfinder, which unfortunately never got funded.
The primary challenges are keeping the components of the array in fixed locations relative to each other. Any deviation of microns would need to be accounted for when combining the images from multiple telescopes. Deep space, far from gravitational interference, is thus the best place to put one of these telescopes.
For an update on the biggest and bestest planned and funded spacebased telescope, check out the Webb Telescope, a replacement of sorts for Hubble.
Now, you couldn't directly see life on another planet (if you are imagining resolving cities from light years away, that isn't really a thing). But certain characteristics of an atmosphere would be a dead giveaway that there was life. For example, an atmosphere with lots of free oxygen is likely to be maintained by life, since oxygen is so reactive that it will interact with pretty much any sort of lithosphere rather quickly in geological time.
If your interferometer can resolve a planet at that distance, then, provided it can detect the appropriate wavelengths, determine the composition of the atmosphere through spectroscopy.