Sounds to me like you have several options:
1) Migrate the app to your existing WAS install, for which you can use the migration toolkit:
https://www.ibm.com/developerworks/library/mw-1701-was-migration/index.html
https://developer.ibm.com/wasdev/docs/migration/
2) Migrate the app to WAS Liberty (note, Liberty does not come packaged with your WAS installation, but you can trivially download it at the first link below) and use its Admin Center to administer the application:
https://developer.ibm.com/wasdev/downloads/download-latest-stable-websphere-liberty-runtime/
https://www.ibm.com/developerworks/library/mw-1701-was-migration/index.html
https://developer.ibm.com/wasdev/docs/move-applications-liberty-using-migration-toolkit/
3) Migrate the app to WAS Liberty and use your existing Admin Console to manage the app:
https://developer.ibm.com/wasdev/downloads/download-latest-stable-websphere-liberty-runtime/
https://www.ibm.com/developerworks/library/mw-1701-was-migration/index.html
https://developer.ibm.com/wasdev/docs/move-applications-liberty-using-migration-toolkit/
https://www.ibm.com/support/knowledgecenter/en/SSAW57_8.5.5/com.ibm.websphere.nd.doc/ae/twve_mwscreatex.html
https://www.ibm.com/support/knowledgecenter/en/SSAW57_8.5.5/com.ibm.websphere.nd.doc/ae/twve_mwsliberty.html
4) Leave the app on Tomcat and use your existing Admin Console to manage the app:
https://www.ibm.com/support/knowledgecenter/en/SSAW57_8.5.5/com.ibm.websphere.nd.doc/ae/twve_mwscreatex.html
https://www.ibm.com/support/knowledgecenter/en/SSAW57_8.5.5/com.ibm.websphere.nd.doc/ae/twve_mwstomcat.html