If an individual fails to improve after you have had a courageous conversation, the issue can become a little more serious and need to be addressed differently.

The most important thing you should do is gather a ‘case file’ regarding the employee

A case file is essentially building a portfolio of evidence regarding their behaviour or performance alongside any discussions you have had with them and agreed action.  It will include things such as what have they done, when, when have you spoken to them, what have you asked them to do, stats, figures, complaints, comments etc.

This evidence will allow you to deal objectively with the situation should it become necessary to take disciplinary action.  You may wish to seek HR advice to support you at this point also.