The current version of the Vesta control panel supports has gzip compiled into NGinx, however, the gzip types are listed incorrectly. To enable compression for NGinx (which if switched on is serving your website rather than Apache) you need to:

1. SSH into your server

2. Type: nano /etc/nginx/nginx.conf

3. Find where it says gzip_types

4. Replace the gzip_types entry up to the next semi colon (next line) with the following:

gzip_types text/plain text/css application/json application/javascript text/xml application/xml application/xml+rss text/javascript image/svg+xml application/x-font-ttf font/opentype;

5. To Save Type: CTRL O

6. To Quit Type: CTRL X

7. To restart nginx: service nginx restart