The correct answer is A. nervous.
The staff have felt on edge ever since they heard the rumour about retrenchment. This means that they are feeling anxious and worried about what might happen. They may be concerned about losing their jobs, or about how they will be able to support themselves and their families if they are retrenched.
The other options are not as accurate. Option B, unhappy, does not capture the sense of anxiety and worry that the staff are feeling. Option C, disheartened, suggests that the staff are disappointed or discouraged, but this does not seem to be the case. Option D, scared, is a possibility, but it is not as likely as option A.
In conclusion, the correct answer is A. nervous.