All believers in Jesus are priests and saints. ( See 1 Peter 2:5)
The psalmist here as used three very unique priests from the Old Testament Moses, Aaron and Samuel who perhaps can help us understand better the role of priesthood in church and life.
Priests in the Old Testament were males who came from the line of Levi and represented their people before God. They offered gifts and sacrifices for sins of the people. Priests taught the law and helped the people with the interpretation of the Law in their daily living.
When Jesus came, He provided a new covenant (deal) for us when it came to the role of priesthood. Now, none of us ( believers) needs a mediator any longer for we can approach God through Jesus our high priest. It is true that we are one body and like that we are not independent, so we are to use our gifts and talents to help make disciples in all nations and live together in harmony and peace.
Yes, there are leaders and elders in churches nowadays, but all those seemingly appearing big titles come under one name that of Servanthood. Priesthood is about praying and serving with and to one another in the Lord.
Mostly it’s about prayer, God’s presence and walking with God.