So, to begin, this is really hard to do, and it can lead to the end of your career at a place. Managers might think of you as That Guy, the one who is always coming out with disruptive ideas. ("Disrupt" ain't a positive term, here.) That Guy makes the manager's job harder because the manager wants a unified front, not debate.
1. It helps if the language interoperates well with the existing platform. If you're at a Java shop, consider Scala and Clojure. Don't bother trying to sell it on Haskell; that'll never happen. But, for Scala or Clojure, the top 25% of Java developers are probably headed that way already.
2. Don't ask permission of nontechnical management. (Grace Hopper: it is better to ask for forgiveness than permission.) Just deliver something cool in it that the rest of the organization can use. In the JVM ecosystem, no one needs to know that the JAR actually contains Clojure code. Get enough momentum behind the project that management actively wants you to demo it to the rest of the company. Then mention the "secret weapon".
3. After (2), get a job ad posted in the new language. The quality of applicants will be a lot better. Post a Java job ad, and you'll get more responses, but your phone-screen-to-hire rate will be about 2-5%. For a Clojure job, it'll be closer to 30%-- and 60% of those who actually know Clojure (those who don't will fail-fast on the phone screen). Not only can you reduce time wasted with unqualified candidates, but you're more likely to get a 10X hire. Now you can make the argument that it's worth hiring more people in the newer, better language.
You're not going to turn a large Java shop into a Clojure company. It just won't happen. But if you do the above and have a bit of luck, you might carve out a CoE (Center of Excellence, also known as an "honor's college", which tends to be an elite suborganization that has an R&D flavor) in the organization that uses it.
That above only works if your company has generally good management. (They don't need to be programming language specialists, but they need to be good at their jobs.) If not, you're not going to get anywhere no matter what you do and it's not your fault. Then, the best bet is to move on.