Adding new SH in the existing SH cluster not replicating the "Distributed Search peers".
Please check and verify if below configuration is there in server.conf:
disabled = false
replicate_search_peers = true
Removed the distsearch.conf(list of all peers and add the above setting in all SH member and restart. After that adding new peers will automatically replicate to each member in Searchhead cluster. Only you need to add it to the captain.