The clicking appears together with the voice singing. When the voice is silent, the clicking goes away. Could it be a problem with the sound recording level, instead.
If AF-S is done in liveview mode, you only have contrast AF on a DSLR, which can make AF-S more stuttering and noisy. A microphone, close to the lens will record all sorts of noise, and what's almost imperceptible to us when recording, will become annoying when playing back the recording.