This is likely caused by insecure content. WordPress is serving resources (images, stylesheets or scripts) over http instead of https.
To resolve this try the following plugins:
Basic SSL setup for WordPress:
https://en-ca.wordpress.org/plugins/really-simple-ssl/
This one will find any internal link/resource request over http and change to https.
https://en-ca.wordpress.org/plugins/ssl-insecure-content-fixer/