What is the best program for an over 40 year old male to gain muscle?
The best approach will always be based upon science.
67-85% of your 1RM are the ranges one should be training at in order to increase muscle size. These guidelines along with eating the proper amount of macronutrients and proper rest will put on you the path to hypertrophy.
Speak with your trainer. I am sure he/she will be able to assist you in reaching your fitness goals.