If you have access to the feed and the server it resides on you can simply add episodes and re-publish it: for thisl access to the feed is regarded as sufficient proof of ownership.
However if you don't have access to the Apple ID and its password that were used to submit the feed originally, you cannot access the statistics nor other facilities in Podcasts Connect. Apart from the statistics, you wouldn't be able to take action if there was a problem. If you have access to the ID then you can just continue as your are.
However if you don't have access to the server and need to move the feed to a different one your will need to get the people currently running the podcast to go through the process described here:
http://wilmut.uk/move
If you want to transfer ownership of the podcast to you own Apple ID you will have to get the owners of the ID currently in use to follow the procedure described in the answer to this post:
https://discussions.apple.com/thread/251807133
As you see all the methods described above require the co-operation of the people who have been running your podcast. If for some reason they are unable to co-operate you will have to start again from scratch - though the original podcast will remain in place as obviously only the owners can request its removal (though if the server is closed and the feed goes dead it will be removed fairly promptly).