The actor portrays a fictional American-born pontiff, Pope Pius XIII, in the new 10-part series set to air on Sky Atlantic.
The Young Pope will get its world premiere at the 73rd Venice Film Festival this weekend.
Hollywood actress Diane Keaton, who plays a nun called Sister Mary, is shown cupping Law's face telling him: "I see Christ's reflection in you."
The series will tell "the controversial story of the beginning of Pius XIII's Pontificate, born Lenny Belardo''.
Italian filmmaker Paolo Sorrentino is the creator and director of the series.
Talking about Law's character and his place in the Vatican, he said: "The most mysterious and contradictory figure of all turns out to be Pius XIII himself.
"Shrewd and naive, old-fashioned and yet very modern, doubtful and resolute, ironic, pedantic, hurt and ruthless, Pius XIII tries to walk the long path of human loneliness to find a God for mankind. And for himself."
The trailer portrays Law's Belardo character as a chain-smoking, brooding man of the cloth who says: "I'm a contradiction and God. Saint. Sinner. Pope. Man."
L.A. Confidential star James Cromwell also stars in the new series as Cardinal Michael Spencer.