In order to be successful you need to be able to fix problems, be flexible and travel all the time. You will encounter a wide variety of challenges on the job, and regardless of your background or skill set, you need to fix them and deliver whatever your manager or client requires. Additionally, you need to be flexible in what you do and where you do it. Consultants travel every week. We encounter all kinds of airport/hotel issues along with the usual living items. If you can do these things, you’ll do great. One big overall item for career success is to keep learning and building skills on every engagement. You have to keep your skills fresh so you are eternally valuable to your manager and partner. As much as all companies claim they have training and skill development programs, the superior performers figure out how to continue learn and deliver.
The ability to actively listen to your client, put yourself in their shoes and anticipate issues before the client experiences them will be key to success as a consultant.
Know the client's business - how they do it, why they do it, who are their customers? Take notes, do your research, ask thoughtful questions.
Flexibility in providing solutions will also be extremely important. Sometimes solutions are black and white but other times they are more grey. How the client will apply your consulting will determine your recommendations.