Since working visas are tied to a single employer, you need to apply for change of sponsorship before starting a new job. Otherwise, you'll be working illegally.
Below are some details on the process taken from Emigra's HK visa handbook:
Change of sponsorship applications (i.e. seeking to change from one employer to another) follow very similar procedural methodologies and consideration processes as change of status applications, involve Forms ID91 and ID428B and are processed via the 5th Floor of the Immigration Tower instead of the 24th. The approvability test is just as onerous, however, and no significant advantage is given to an applicant merely because he is in possession of an employment visa sponsored by a previous employer. In general terms, however, if the new employment is in exactly the same field as the original employment and the 'weight' of the employers is similar, change of sponsorship approvals are usually quite readily forthcoming. Also, the longer the change of sponsorship applicant has been in Hong Kong the more accommodating the Immigration Department are in granting approvals to change employers. The Immigration Department states however, as a matter of policy, that such applications are not normally considered or approved. Current practice suggests otherwise but it should be remembered at all times that any such change of sponsorship approvals represent a positive act of discretion on the part of the Director of Immigration and his consent to change sponsoring employers should not be viewed as a matter of legal right.