Need a social media policy for your work. The one produced here by the Dept. of Finance would be a very good starting point.
The ABC one is also good, and has four basic standards
1. Do not mix the professional and the personal in ways likely to bring the ABC into disrepute.
2. Do not undermine your effectiveness at work.
3. Do not imply ABC endorsement of your personal views.
4. Do not disclose confidential information obtained through work.