Various church traditions do service leading differently. Some have a minister of music leading the services. Some have chairmen leading the service. Some have the pastor leading the service. And I’m sure there are others ways in addition to these.
If you’ve listened to Sinclair Ferguson for any time you may have heard him talk about Christ as the service leader, the service conductor. In Hebrews 8.1-2 it says “we have such a high priest, one who is seated at the right hand of the throne of the Majesty in heaven, a minister in the holy places, in the true tent that the Lord set up, not man.” The greek word for ‘minister’ is where the english word for liturgy comes from. So Christ is the great liturgist who leads his people in the praise and worship of God.
Recently reading some Hugh Martin, he applies this idea back into the death of Christ. Christ, in his sacrifice on the cross, was “conducting the glorious service at the unseen altar of God, and positively there offering up himself by his own intensely active will and deed.” I don’t know that I’ve ever thought of the cross as a worship service. A worship service to God, making an offering to God, and Christ is the service leader, the Priest, leading his people to God and inviting them into the presence of God, to follow him within the veil.