You can use existing Java code from Kotlin and vice versa. A mix of Kotlin code, Java code and Java libraries in the same project is easily possible.
A very important feature of Kotlin is an extremely extensive interoperability with Java. Especially valuable is that in Kotlin you can continue to use just about any existing Java framework and Java libraries as usual.
So you do not have to go without slf4j, Guava, Apache Commons, Tomcat, Jetty and the countless other gems of the Java ecosystem!
The Kotlin compiler can (simply put) handle both Kotlin code and existing Java code. Thus, it is easily possible to use both languages in the same project.
In particular, during your transition to Kotlin, and with a (large) existing Java codebase, it is a real plus that you are not forced to convert proven code. Rather, it makes sense to develop new components in Kotlin, while easily accessing your current Java code.
Of course, one can later convert existing Java code to Kotlin to take advantage of its many advantages. For this purpose there are tools/plugins that convert Java code into Kotlin code fully automatically. This works very well in most cases, although often less than ideal Kotlin code is generated, and a little fine-tuning is advised.
Kotlin at runtime
Basically, the only difference at runtime on the JVM is that you need to include an additional .jar library (kotlin-stdlib.jar) - nothing else.