What is the ruling on the regular Imam presenting another person to lead the worshippers in Tarawih prayer due to his beautiful voice and his mastery of melodious recitation of the Quran? And does that diminish the reward of my prayers?

There is no harm in another imam leading the people in Tarawih prayer, other than the regular imam who led them in the Isha prayer, but on the condition that the regular imam grants permission for that; because he has more right to lead the Tarawih prayer. The reward for the prayer is not diminished by the variety of imams, as the Companions used to pray Tarawih behind more than one imam.