Is it possible to work in Singapore if the employer applies you a work permit in Hong Kong?

It depends on what "work" means in your case. There are business travelers everyday going overseas to do some work, and even when they are working inside a foreign country, they are still doing working for and on behalf of their own company and not for any foreign company. Any work visa issued in Hong Kong only applies to employment within the city of Hong Kong and can't apply in Singapore, and vice versa. With a HK work permit you can still "work" in Singapore as a representative from your Hong Kong office, but you cannot stay in Singapore for more than 6 months out of every year, and need to maintain residence in Hong Kong throughout your permit.