A key aspect of Clojure is its interoperability with
Java. You can write Clojure that exposes a traditional Java class API and you can package Clojure in a JAR file and use it in your Java world, just like any other library. Clojure itself is packaged as such a JAR file - Clojure 1.4.0's JAR file is about 3.4MB - and pretty much all pure Clojure libraries are tiny (just a few KB) because they're mostly distributed as source (and compiled to bytecode on first use in an application). This means you can use Clojure for any subcomponent of your system, design a class API for that and implement it entirely in Clojure, then package and distribute it to your colleagues, without them even needing to know it's not "Java Inside".
Similarly Clojure can interact with any existing Java libraries you already have so you don't need to reinvent any wheels - Clojure fits in on top of everything you already have, as well as being able to fit in underneath your existing Java infrastructure.
Perhaps one of Clojure's most powerful features is the ability to develop interactively in the REPL, allowing you to quickly build scripts and manipulate existing Java libraries and infrastructure in ways that simply are not possible in Java. Imagine demoing a Swing-based GUI to business stakeholders and being able to interactively modify it in real time, accepting their feedback, while the app is running? At that point they'll know it's not Java but they'll be impressed enough to want this new technology anyway.