Your boss is the lynchpin of your work experience. A great manager can make the most horrible job tolerable, or greatly enhance fulfilling work. When a good manager leaves, she can take the best parts of the job with her. When she does, employees need to honestly assess the new manager, their own jobs and how likely it is that the management shake-up will directly affect their work.
When a good manager or boss leaves the organization, remaining employees need to assess the person stepping into those managerial shoes fairly and critically. Determine if the new manager can handle the workload of the previous one and closely examine how she treats employees. A good manager is worth her weight in gold, but don't rule out her replacement just because she isn't as likeable. Instead, pay attention to results and note how the new manager makes you feel. Job satisfaction is critical to your happiness. If you feel mistreated or abused by a new manager, you may need to assess your employment situation.
Just because a less-liked replacement has taken your favorite manager's position doesn't mean it's time to start forming an exit strategy. Assess how much the new manager, good or bad, actually affects your work. New managers enter organizations with different agendas and priorities. Even a manager much less competent or personable than your previous boss might leave your department alone. Keep an ear to the ground to learn the new manager's priorities and determine how they might personally affect you.
If a new manager truly is someone with whom you cannot work, begin forming an exit strategy. Start discreetly circulating your resume. This is the time for serious self-assessment. Perhaps your previous boss made a horrible job bearable, and that's why you adored her. Or maybe you loved the work and a wonderful boss was simply a great bonus. Make a decision about whether to stay in your current industry. That will determine where you send your resume and which direction your exit strategy takes you.
Realize that the new manager faces an entirely new organization and corporate culture. He doesn’t yet know everyone's name like your old manager did, and the things you assume someone entering the company should know might not be as self-evident to the new person. The key is to give the assessment process time. Begin planning your exit if you must, but don't make any rash moves just because the new manager's first few weeks are tense. Also, if you're set on staying in your current industry, consider contacting your old boss for help. If she was as good as you think she was, she might lend a helping hand in the job search, or even consider taking you along as she moves to a new company.