START WITH and CONNECT BY condition in Oracle SQL
When you have CONNECT BY without START WITH, the root, starting points of the recursion are all the rows of the table. It is useful if you want to find all the hierarchies under all employees. 

The condition in CONNECT BY is checked only for the next levels of recursion, so only for siblings.

You can modify START WITH to get everything except Cambrault:
(note that this way, an employee may appear multiple times, one as individual, one as a child of their manager, another as a child of their manager, another as a grandchild of their manager's manager, etc.
(so this is probably not what you want):  

START WITH 
      NOT (last_name = 'Cambrault' AND first_name = 'Gerald')


or all hierarchies under top level managers (employers without a manager). Everyone will appear once this way:

START WITH manager_id IS NULL


or all hierarchies under top level managers (employers without a manager) except Cambrault's.
Note that this will give you the same results as the previous START WITH with current data (but will differ when Cambrault is promoted to top level manager):

START WITH manager_id IS NULL
  AND NOT (last_name = 'Cambrault' AND first_name = 'Gerald')


Test in dbfiddle.uk.