Although I don’t have any trainers working for me I have however worked with other trainers and staff to accomplish certain tasks. Your mission statement is something that is unique to your business model and reflects your philosophy.
Whoever you decide to hire for this position, he/she must understand that they will be part of a team and leading by example is a very essential part of this position. You are the one who defines the mission statement especially if this is your gym/business. If not, then the owner must have this in place already if this business is to survive and set itself apart from the competition. All the employees must live by and respect that mission statement because that is the core and heart of the business. The directors/managers in place must make sure they understand that and then help those who work under them to do the same.
Any director/manager (no matter the department) must be a good leader. To do this they must have certain qualities that will establish them as leaders, so others can listen and respect them. They have to be good listeners, know and care about each of the people who work under them, be good delegators, lead from the from and set the pace. Each person has their own plus and minus, but at the end the have to be great team players.
The Director of Personal Training must have the qualifications (good leadership, certifications, education and personal experience) the are required to perform this job and be able to manage and lead a team of other trainers who most likely think they are right all the time ;-)! He/she must be able in selling PT sessions and know which client to give to what trainer. He/she needs to have some good level of understanding psychology because this is what will make his team of trainers successful or not. Understanding each trainer under them and then be able to match them with the right client could determine if that department will be a strong one or not. The PT Director must be quick in assessing difficult situations and solve any issues that rise with diplomacy and swiftness. PT is a big part of any gym and having the right person at this position could make or brake that business. Great trainers add value to the business and having the right parson leading them is an important task. Your hiring process should be a great opportunity for you (or whoever the owner is) to find out if the candidates for this position have the right attitude and experience to perform this job. Also, if they understand the mission statement of your organization and how well they can adjust their organizational skills to comply with it.
I hope this helps. There are many great and successful PT mangers here who can give you better advice than mine and even some more helpful tips :-)! Good luck.