Does Christianity claim itself to be the final revelation from God? Does Christianity claim to be the last true religion that will ever exist, or does it admit the possibility of being supplanted by a new revelation, like Judaism was with Christianity?
Christianity1 doesn't make claims about itself but rather makes claims about Jesus. And those claims are based on the Bible, which records Jesus' own words. So what does Jesus say about being supplanted by a new revelation? He was asked exactly this question - here is His answer:

When the men came to Jesus, they said, ‘John the Baptist sent us to you to ask, “Are you the one who is to come, or should we expect someone else?”’
At that very time Jesus cured many who had diseases, illnesses and evil spirits, and gave sight to many who were blind.  So he replied to the messengers, ‘Go back and report to John what you have seen and heard: the blind receive sight, the lame walk, those who have leprosy are cleansed, the deaf hear, the dead are raised, and the good news is proclaimed to the poor.  Blessed is anyone who does not stumble on account of me.’

Luke 7:20-23
Furthermore, in another place He specifically says that there is no other way to God than through Him:

Jesus answered, ‘I am the way and the truth and the life. No one comes to the Father except through me.

John 14:6
So He's the First Revelation and The Last. As Peter said2, &quot;There is no one else.&quot;
1 And here you'd have to specify which flavour of Christianity you're talking about.
2 My paraphrase.