Graham Dietz's Answer:
There are things that a newly arrived manager can do to establish their credibility, and to motivate their new team. Getting your new team to trust you is a great start.
In a 'climate' of trust people work better together, and enjoy their work more. American research has found that hotels where employees trust their boss were substantially more profitable than those whose managers scored average or worse on trustworthiness. Without trust, however, workplaces can be dismal prisons, and trust's absence usually hits the bottom line hard: poor collaboration, scant communication, constant belittling monitoring…
Your new team members are suspicious of supervisors in general, perhaps justifiably so. This will have shaped their 'default position' toward you. So you must re-build their trust in managers, which is much harder than initial trust-building. But, you are new. You can turn that to your advantage, and set about the relatively easier task of building your own reserves of trust from 'scratch'. Put simply, your challenge is to separate yourself and your way of working from what happened in the past, and to establish a new culture based on trust.
First, point this separation out to them. Suggest gently how self-defeating it is to assume that all managers are alike, and to expect the worst. If this were true, how would organisations ever change? Ask to be judged on your merits and deeds. Draw a line. That was then; you are now.
Being trustworthy is based on three attributes: competence, benevolence and integrity. Display these three attributes consistently, and demand them of your new team. Trust is a matter of promising what you can deliver on these three, and delivering them consistently. And if for some reason you cannot deliver, you need to explain why early and honestly.
You want everyone in the branch to perform well in their job; anyone who feels that they are in danger of not satisfying their job requirements should seek your help. (Give everyone a clean slate, and a chance.) Then show how good you are at your job: hit your targets, reward everyone who hits or exceeds theirs, keep your word, inspire your team, deal with personal and technical problems fairly and well. All of this reinforces the 'ability' dimension.
You want everyone to share the same motive for success, and work for it. This is the 'benevolence' dimension. It is not a hippy kind of love; it is about shared motives and respect. Set demanding but achievable branch-wide targets and then related personal targets. You also want everyone to treat each other with respect and to collaborate; you will not tolerate any abuse or unproductive antagonism. Not everyone will get on at work, of course, but these inevitable conflicts should not be allowed to affect their work. Benevolence can accommodate 'agreeing to disagree', but not hostility, back-biting and cynicism.
Finally, you want everyone to be honest with each other (which is not the same thing as being tactless and cruel), to back up their words with actions, to treat everyone equally. This is 'integrity'.
Trust shapes a performance culture. To be able to trust someone is a great feeling (not to mention a relief), and it is a source of pride and obligation to be trusted. Make clear that those who don't want to trust or be trusted, or those who abuse others' trust, will not survive long in your branch. (That includes you.)
So there can be neither favourites nor victims; just people who do their job well and are rewarded for it, people who can't but who seek and receive help, and people who don't do their job well and don't want to change who must then leave. Tolerating under-performers will undermine your integrity, not to mention your competence; to fail to help them will undermine impressions of your benevolence. So, give people a chance, support and time to turn their performance round, but if they cannot change, help them leave with dignity.
This new set of values and behaviours will take time to establish, and there will be relationship blow-ups and the occasional cock-up, but if you believe in the merits of trust, believe in your own trustworthiness, give everyone a chance to demonstrate theirs, maintain commitment to it constantly, you should reap the rewards.