MySQL Triggers Different Database Different Server
There's the FEDERATED storage engine, which makes for a way to create a "proxy" table in your database server, which points to a real table on another server.

FEDERATED is disabled by default. To enable it, add this to your my.cnf configuration file, under the [mysqld] section:

federated = 1


So your trigger on some table T would then INSERT into your FEDERATED table FT, which would connect to the remote server, pass credentials, and perform the operation.

Do note the overhead: triggers are by themselves performance killers. Add to that the connection to the remote machine, and you now also have latency to worry about.