In The Scarlet Letter, what possibilities are given for Dimmesdale's career if he and Hester left Boston.

In chapter XVII of The Scarlet Letter, titled "The Pastor and His Parishioner", Reverend Dimmesdale is walking in the forest, as he often does out of his perennial feeling of guilt, when he hears the voice of Hester Prynne call his name.

Hester asks Dimmesdale whether he has found "peace", and he responds that he has not and that if he were an atheist he probably would not be as disturbed as he feels, being that he is a man of God who carries a horrible secret. He says that he is miserable and that he lives in torment.

Even though Dimmesdale has not suffered even a fragment of what Hester has, it is she who comes forth to offer succor.

"The people reverence thee," said Hester. "And surely thou workest good among them! Doth this bring thee no comfort?"

Interestingly, Dimmesdale's first preocupation is the opinion of the people toward him if they ever find out his secret. This is much more important to him than his responsibility toward Hester.

Hester, who has always supported Dimmesdale, once again comes forth with a plan. One, which would allow Dimmesdale to keep his vain desire to shallowly please people. However, this plan includes her. She wants to be with Dimmesdale, and bring their daughter, as well. She gives him a good talk about it and, from what the reader can conclude, she succeeds in convincing him, albeit, at the beginning. 

Leave this wreck and ruin here where it hath happened. Meddle no more with it! Begin all anew! Hast thou exhausted possibility in the failure of this one trial?

Hester is correct. To feel superior among a group of blind followers is no deed at all. Therefore, why not start over somewhere more challenging and exciting; just somewhere different. 

 Be [..] the teacher and apostle of the red men. Or[...] be a scholar and a sage among the wisest and the most renowned of the cultivated world. Preach! Write! Act! Do anything, save to lie down and die! [...] make thyself another, and a high one, such as thou canst wear without fear or shame. 

With those words, "preach", "write", and "act", Hester shows Dimmesdale that he has a lot to offer. He can evangelize the natives, become a professor, even become a full scholar. He has options. Hester wants to be a part of those options, which is the reason why she so fervently suggests them. 

We will find out that the idea was still too much for Dimmesdale to handle, and he could only take as much of it as he could. He tried his best to come to terms with it but, in the end, he decides to give it up and die at his own will at the scaffold.