He teleports from town to town, instantaneously. He doesn't need to travel there. One second he's chilling out in Duglad Aisle. Next he's at Bangor. Other characters have shown to possess this ability, but they were usually incredibly powerful druids, magic fomor beings, or demi-gods. However, Redire alone has shown that he is the Tuatha De Danaan only normal who is capable of this amazing skill.
Fleta and Pierrick has proven to be able to pop in and out, but only in fixed locations. This is most likely due to the use of items.
However, Redire is not a man bound by the rules. His bad assery is only limited by, say, a broken leg caused by the Guardian of Ancient Wisdom put together by gold alloy. He was the leader of the paladins, slayer of thousands of fomors, defender of justice, and he freaking raised two goblins and tamed them into society.
In G2, once you unfoil Esras's evil plots, Redire instantly sends you to the lobby of Bangor. While its true that he could've done this with the help of a dungeon wing, what comes next is the real magical trick. He tells you that he will go ahead first, however once he leaves you will be confronted by a long dungeon full of closed doors that don't seem to have been passed already. Monsters are crawling everywhere, the doors are locked, and the only way to pass is to destroy every last one of these fomors.
Once you arrive at the boss room, you see that Redire has already been there, and for some time. He was already in a heated discussion with Esras. How did he get there? Instant Transmission of course. When he is injured by Tabhartas, he tells you not to sacrifice yourself and run away. Its true that Price is a brave man who wouldn't force you to stay against your will to fight, but why did he really want you to leave when he knows you are the only hope left to stop Esras and save Erinn? Because you're NOT the last hope. First off, he could've instant transmissioned himself out of the place in case of a true emergency, thus there was no need for you to stay and protect him had he really needed to run. Second, he really just wanted you out of there so you wouldn't witness the destructive power of a man who was able to slaughter thousands of fomors without even being "knocked out" once. He was ready to beat the golem down with his bare hands, its just you happen to interrupt by turning into the Knight of Light. From there he just watched to assess your abilities.
In G3, you will often see NPC's entering dungeons. However, when Redire is seen, he actually enters FROM the inside of the dungeon, NOT the outside. How the heck does that even work? He obviously teleported there. And then there is a cutscene where he is seen with a large army of goblins. In the very next scene, you see all the goblins on the ground. Dead.
Later in G3, you find yourself baited into a trap in the midst of Alby dungeon, surrounded by a dozen of Ghost Armors, Ruairi, AND the demi-god Cichol himself. Right before Cichol's dark magic is about to finish you off, Redire appears. Out of nowhere. Standing right next to you. The doors to the room closed, no fomors noticing his appearance until he is right there. Everyone is confused. Redire gives a smiling face, chuckles simply, grabs you, and the next thing you see before you eyes? Emain Macha.
"We should be safe for now", he says.
How?
Instant Transmission. Thats how. He grabbed you and blew out of there.
Thats right. Redire is the first and only man in Erinn to have learned and mastered the ancient arts of Instant Transmission. There is enough proof of this. He was also the 5th Tuatha De Danaan to ever see Morrighan. Obviously, she only allowed him this gift because he has mastered such a powerful ability.

There is no doubting it. Redire's power level is over 9000.

TataraKogasa (46 Nen) Grind'an Dungeons
Margatroid (47 Witch) Looking for Oil Bomb Brawlers to party with.
S> Ghost Racer, 950k.
S> Junk Fighter Avas, 400k Each