Is Three some sort of priest?
I would have to say he was not a priest, although this may still be proven wrong since Season 2 has not come out. From Hamatora's wiki, I was only able to find out this much information...


  He once planted a bomb to destroy his enemies in HQ which resulted in him accidentally blowing up some of the orphans he looked over. With extreme guilt, he felt that he should raise the kids to kill him.


I believe the bible is meant to reflect on his guilt over the killings of the orphans, based on the fact that...


  Three has the power to unleash his inner beast by holding a Bible and asking the Lord for forgiveness. By doing this, he becomes extremely strong.


I believe the true intent of this is to show Three's guilt for his actions by using the bible as a vector.