How to get to Leiyang city from Singapore?

As I know, there is direct flight between Singapore and Changsha. So you can fly into Changsha first. Then take the bullet train at Changsha South Train Station to Leiyang in around an hour. However, the plane does not operate every day. I suggest you refer to the website to know whether it is in service for your travel date;
https://www.travelchinaguide.com/china-flights/