What is the duty of the Imam who led the people in the 'Isha prayer in a commercial complex, then heard the sound of music coming from the complex; should he interrupt his prayer?

The fundamental principle is that whoever begins a fard (obligatory) act of worship must complete it. It is not permissible to interrupt an obligatory act of worship after starting it, except for a legitimate Shar'i reason, such as killing a snake or aiding someone in distress. This is based on the Almighty's saying: {And do not invalidate your deeds} [Muhammad: 33].

None of the scholars has stated that seeing or hearing a reprehensible act (munkar) is a justification for interrupting a fard prayer. Therefore, if the sound of music suddenly reaches the worshipper, it is obligatory for him to continue his prayer, turn his heart away from the music, and strive to achieve khushu' (devotional humility) in it. He is not sinful as long as he disapproves of the reprehensible act in his heart, and then denounces it after completing his prayer, to the best of his ability.

However, if the sound of music prevents him from performing the prayer correctly, or interferes with its pillars or obligatory parts, then he should interrupt the prayer at that point and perform it in another place where he can complete it.