The most often overlooked tool in the career toolbox? Knowing when to move on.

Having a successful profession is no longer just about how smart you are or how capable, but how you pull the plug when things don’t work your way.

Several LinkedIn Influencers this week weighed in on how to be tough and start anew — without damaging former connections. Here’s what three of them had to say.

Sallie Krawcheck, Business Leader of Ellevate Network

“In the early days of your career, success may be driven by how smart or clever you are. But before very long, success is driven by how resilient you are,” wrote Krawcheck in her post My Secrets to Resilience. “Success is about how many times you get back up. Believe me, I know. I’ve been fired publicly….twice.”

Resilience, in part, comes from lasting relationships forged even during the toughest work scenarios.  If someone has helped you, make sure you repay the favour in the future.

“I feel a responsibility to the people who’ve helped me,” stated Krawcheck. “There was the senior analyst who mentored me, the boss who hired me when no-one else would, the boss who gave me my first big promotion when I was hugely pregnant, the scholarship program that paid for my education… Each of these people took risks with me, and in turn I feel an on-going responsibility to them.”

Resilience also comes in many forms. “I listen to the critics…but I don’t dwell,” she wrote. “I work hard to receive negative feedback well…but I also recognise that it’s a lot easier to criticise than it is to actually do…I take the feedback from the ‘doers’ much more seriously than from the Greek chorus.”

Most importantly however, learning to be resilient was simply a lesson in appreciating the good and not dwelling on the bad.  Krawcheck wrote that “I’ve loved my jobs. Even on days that I hated them, I loved them.”

Angela Ahrendts, Senior Vice President of Apple Retail

New jobs always come with their share of stress. You are trying to prove yourself, learn a new way of doing things and finesse the company culture. But there are some ways to manage this stress and soar, said Ahrendts.

“I am by no means an expert at these transitions, but I’ve always tried to be consistent in how I run, exit and begin in a new business,” stated Ahrendts in her post Starting Anew.

Firstly, it’s important to “stay in your lane,” wrote Ahrendts. “You’ve been hired because you bring a certain expertise to the team and the company. Try to resist putting additional or undue pressure on yourself trying to learn it all from day one.”

“It's human nature to feel insecure about everything you ‘don't know,’” she added. “By staying focused on your core competencies you will be able to contribute much sooner, add greater value long term, and enjoy and have more peace especially in the early days.”

Secondly, “‘Ask questions, don’t make assumptions.’ Questions invite conversations, stimulate thinking, break down barriers,” Ahrendts stated. “Questions show humility, acknowledgement and respect for the past, and give you greater insights into both the business and individuals… don’t be afraid to ask personal questions or share a few of your personal details.”

What to do then, when all else fails?

“Trust your instincts and emotions. Let them guide you in every situation; they will not fail you,” advised Ahrendts. “Never will your objectivity be as clear or your instincts sharper than in the first 30 to 90 days. Cherish this time and fight the urge to overthink. Real human dialogue and interaction where you can feel and be felt will be invaluable as your vision, enabled by your instincts, becomes clearer.”

Johnny Tillquist, Founder of Svenska Jobb Utomlands

Sometimes, there isn’t even time to plan for smooth transitions. Tillquist wrote in his post Quitting Your Job: Without Security? on how to proceed and start anew.

“Many people today are not happy or satisfied with their current workplace. It could be the working culture in the company, unsatisfying responsibilities or a bad boss (even a combination of them all),” wrote Tillquist.

“When you resign a few things happens usually, some colleagues may change their behaviour for better or worse. You could also end up with a lot of not-so-funny tasks all of the sudden,” Tillquist stated. “Some will be sad to see you leave and you might feel the same way (never burn the bridges).”

After your final day has passed, the real work begins.

“You saved up some money to cover expenses for a while and you begin exploring various jobs available matching your experience. It’s not easy and the feeling of I screwed up begins to creep in,” he wrote. “However, when you have nothing to go back to, you become very motivated. It’s amazing how much you can do when under pressure…If you fail, the parachute will not open and that realisation is a huge motivator.”

It may not be easy, but quitting without security isn’t the worst thing that could happen.

“I am not saying everybody should quit their jobs if unsatisfied. I am not saying that it’s wise,” wrote Tillquist. “All I am saying is that resigning without the comfort of a new job on the horizon can be a very rewarding experience if done right…It will give you that push that we sometimes need in order to get things done and also give you some valuable time to figure out what you really want to do.”

How have you dealt with career transitions? Do you have any advice to share? To comment on this story or anything else you have seen on BBC Capital, head over to our Facebook page or message us on Twitter.