First of all, it will be hard to establish that the astrologer was in fact successful in his profession. The narrator says specifically that the astrologer is not a true astrologer:
he had not the least intended to be an astrologer when he began life ; and he knew no more of what was going to happen to others than he knew what was going to happen to himself ... . He was as much a stranger to the stars as were his Innocent customers.
True astrologers in India are most often of the Brahman class who have studied under a guru for extensive periods of time and attained various levels of mastery. So, in the strictest sense, it is not possible to say that the astrologer was a success at his profession because he is what we would call an impostor or a charlatan and not a bonafide member of the profession he claims. Nonetheless, within the text are some indicators for the success the astrologer has as a charlatan astrologer who fools his customers.
The first thing that makes him a success is his attire, both the garments he wears and the religious symbols he paints on his face:
He wound a saffron-coloured turban around his head.
His forehead was resplendent with sacred ash and vermillion.
This colour scheme never failed.
While recognizing that attire is not a personality trait, the narrator’s description of it reveals the astrologer’s personality traits of sagacity (i.e., discernment and judgement) and empathy with (i.e., identifying with) others’ perceptions. This is born out in other parts of the story, for instance when the narrator says the astrologer “said things which pleased and astonished everyone” as a result of (1) studying the person talking, (2) long experience (“practice”), and (3) “shrewd guesswork.” Studying people and “shrewd (i.e., astute, keen) guess work” go hand in hand with the personality traits of sagacity and empathy.
Another personality trait that the narrator reveals is that of feeling true guilt: "I thought I had the blood of a man on my hands all these years." If he did not feel truly guilty for stabbing his acquaintance over a drunken gambling incident, he wouldn’t have had the impetus (i.e., driving force) to make a successful living at something entirely outside the realm of his previous knowledge and experience. In other words, his sense of true guilt made him understand that he dearly needed a good cover and new identity; others may have continued in a path of error and wrong doing.
The astrologer’s closing conversation with his wife reveals another personality trait that contributes to success in his chosen work, that of being able to focus deeply on the thing that is important at the moment. For instance, this personality trait is at work when he listens intently to a new customer: “[he] never opened his mouth till the other had spoken for at least ten minutes.” Another instance of this trait of focusing intently is that after meeting his victim face to face again; after realizing that he is now free of guilt; after deflecting the victim's vengeance; and after making a confession to his shocked wife (“You tried to kill !”), he can still focus on the immediate moment and what is needful in that moment and give himself a good night’s rest so he can be an astrologer again tomorrow.