Hi,
According to your description, I think what you said "always on cluster" refers to the Always On availability groups. Using CDC with an availability group, you need to create CDC jobs on the primary replica or possible primary replica (failover), and only enable it on the primary replica.
Please check the document- Replication, change tracking, & change data capture - Always On availability groups.
You should create the jobs at the new primary replica after failover. The CDC jobs running at the old primary database should be disabled when the local database becomes a secondary database. Post this if the replica becomes primary again, you need to reenable the CDC jobs on the replica. To disable and enable jobs, use the @enabled option of sp_update_job (Transact-SQL). For more information about creating CDC jobs, see sys.sp_cdc_add_job (Transact-SQL).
In addition here is a post about how CDC jobs are always enabled only on the current primary replica.
https://dba.stackexchange.com/questions/139231/cdc-with-alwayson-availability-groups