In actual fact, your employment visa permissions belong to you, not your employer as they are just the sponsor of your immigration status, not the final arbiter of whether you can remain in Hong Kong or not.
Only the Hong Kong Immigration Department hold this power.
If you find your position with your employer untenable and determine to leave your job, effectively, your permission to work ceases at the point of you terminating your employment, but your consents to reside in Hong Kong continue until the Immigration Department tell you otherwise OR your current limit of stay expires.
Consequently, you should write to the HKID and advise them of the change in your circumstances and at the same time let them know about your new intentions in the wake of leaving your job.
It is lawful activity to look for an alternate employer under this scenario, as is interviewing and accepting an offer of employment. But it is NOT lawful to start working for a new employer until you have secured the permission of the HKID to take up that new employment.
To go on to get these permissions, you to make an application to change your employment visa sponsor, which should 4 – 6 weeks to complete after you have submitted your application in light of your new offer of employment.
However, it is important not to assume that your application will automatically be approved as you still need to pass the employment visa approvability test in respect of that alternate employment and for all practical purposes the Immigration Department will treat such an application as an entirely new one.