The key to mentoring a worship leader is to make it happen from the very beginning. If your only option is a organic, home grown leader from within the body mentorship may be crucial for developing people in a short amount of time.
Much like lead pastors who mentor associate pastors and others who desire to be in the ministry, a new or budding worship leader may need to be mentored by leaders who have a good understanding of the daily challenges, organizational issues, recruitment needs, equipment limits that a worship leader faces.
Giving honest and open feedback on a leaders ability to lead a congregation in worship as well as their musical ability and team leadership qualities is crucial and should be done with care and encouragement, preferably by someone who can relate to the challenges of the role.
Many times people are allowed to be in these roles with little to no feedback because there is a lack of knowledge in these areas by a pastor.
Someone having a "willing heart" does not mean they should not be given feedback and direction.
Good questions to ask yourself and your worship leader.
A dry run?
If you do have an internal candidate for the role a good idea may be to have them "audition" for the position by running a mock service complete with the following,
The pastor can then decide if the candidate is ready for a service.