There is no Bible authority for clapping in worship, either in time as part of the singing, or in the form of applause.
Clapping during singing is a form of percussive accompaniment. What is the difference between striking our hands together and striking a drum with our hands? Musically speaking – nothing. The only accompaniment for our singing is to come from the heart (Ephesians 5:19). Also, God is not worshiped with men’s hands (Acts 17:25).
Clapping as applause brings glory and recognition to men, and is not directed toward God. All worship and praise is to be directed toward God. Do they clap when the preacher says something funny or something with which they agree? Will they clap when the song leader does a good job? Will they clap when someone says a good prayer? And what about those for whom no clapping is done? Will they think their worship is inferior or unacceptable because it didn’t warrant applause?
Why not let God reward us for our deeds like the Bible says (Colossians 3:23-24)? Worship is a time to focus our attention and affection upon God, not men. Worship is a time to give reverence and glory to God, not men.