I am not sure what you mean by "believer" but I can answer this question if you mean a Christian. Yes, of course there is room for revenge, and hate, and unforgiveness, and deceit and gossip, and murder, and adultery. Christians aren't perfect, perfection is the destination. Ironically, the only people who have ever lied to my face have been leaders in the church. I knew one pastor who was the town gossip and because he had so much power, he could ruin people by revealing the inside info he knew; something he did regularly. Nobody can confront him because of fear - great pastor. The most vengeful person I ever met was a guy who spent all of his time making sure that he had the perfect "Christian" image to his perceived audience. All this really means is that Christians (or people who think that they are Christians) are capable of any and every sin out there, even the people who are the "best" Christians.
Nevertheless, just because it is possible for a person to harbor revenge does not mean that revenge is acceptable. Anyone who knows the overwhelming forgiveness that God has given to them should forgive others.