At this stage, if not before, your researcher should be honing their field of research, and ensuring that their work is likely to make an original contribution to knowledge.
Much of what you will be doing will be continuing what you have already set up.
Conferences and presentations
Ensure that your researcher makes a formal presentation of their work at departmental seminars, with questions and feedback. To make the most of this encourage your researcher to spend time developing and practicing their presentation and arrange for you or someone suitable to give feedback on style as well as content. Encourage your researcher to attend poster events and conferences for networking opportunities.
Writing up plan
Encourage your researcher to create a writing up plan - remind them that typically this takes longer than expected, so planning in advance is helpful.
Life beyond the doctorate
As your researcher is likely to be more than halfway through their doctorate, encourage them to start thinking beyond it. You don't need to know the answers, but knowing where to direct them might help - your institution's Careers Service can be a useful starting point, as can the careers section of the Vitae website.
Life outside research
Doing a doctorate can become all-consuming, so keep an eye out for an over-worked, stressed researcher. Encourage them to have a life outside their work, and to Vitae's section on staying healthy. Taking a break will help them to come back to their research refreshed, more motivated and productive. A break can also help them to approach their work from a different perspective.
Courses and support
Find out about the courses and support your HEI can provide for researchers during their research and when planning their careers.