Purpose.

He must had been very unwilling to die that he had to ask his brother to find a host for his revival. For what purpose?

Noah family, at first, was said to be immortal. However, it was discovered that that wasn’t the truth. Inside the Ark, Kanda killed Skin Boric—he vanished from the world. In 14th’s case, he was killed by the Earl, but his soul remained. In my humble opinion, I think there are two chances about what he would do if he managed to come back to live:

Revenge

The Order thought that this is the most convincing reason. He had tried to kill the Earl once, but he got killed instead, so it was logical if he wanted to go back to live just to attack the Earl one more time. But if it was for revenge, then what after he had avenged his hatred? Would he just come back to the world of death peacefully, or what?

Helping the Noah

On the other hand, we can see in the Earl’s flashbacks about the 14th. He mentioned that he would always be his brother’s ally whenever he needed him. therefore it is also possible that he would help the Earl to destroy the world.

He finally revealed his secret in chapter 185, where the Earl got Allen and his soul began to take over Allen’s consciousness.

Fourteenth: “I wanted to let you know that I’ve come back. I knew you’d come for me, brother. This time, I will kill you. I’ll kill you, and then become the new Earl of Millenium!

There, everyone heard his purpose. The Black Order’s top guys were there, as well. Komui and Leverrier now learned his purpose. Considering how the 14th wanted to kill the Earl—which means that he would have to slaughter the whole Noah family since they were loyal to their brother—he might need help from the exorcists. He might be stronger if he were to take over Allen’s body, but could he kill 13 guys all by himself? But the combination of a Noah+Allen might be more than expectations, considering how Allen could synchronized with Innocence with a percentage that exceeded 100%.

While the 14th is an ally in case of the order’s mission to defeat the Earl, what he wanted to do afterwards might endanger the Order—or rather, humankind. But if he were to destroy the world, then he would be all alone since the Order would be against him, and the other Noahs were with the current Millenium Earl. It is unclear yet about what he sought. For now, there are far too much mysteries surrounding Allen and the 14th, which hopefully will be answered eventually in the manga.