If I am currently enrolled in the Android Developer Nanodegree program, can I finish this version or do I need to enroll in the new Kotlin program?

You can finish the current version of the program that you are enrolled in to graduate and get the certificate. Students will be required to finish their program by April 13, 2021. There is no requirement to enroll in the other Nanodegree program as both the programs are standalone Nanodegree programs.