1. Researchers and Developers
This type of positions is quite rare in Singapore. I only know a couple of mindef related government agency doing it including DSO, DSTA and CSIT. For commercial firms, I only know Mcafee has some research positions in Singapore.
2. Security product vendor/distributor
These vendors/distributors bring in various type of IT security products and provide sales, support and other value-add services for these products. Some of the examples are MTechpro (distributor for checkpoint firewall etc), Quantiq International.
3. Security service provider
This type will include those big SI (System Integration)companies such as NCS, SCS, HP, IBM etc they have security teams to provide system design, implementations and integrations.Usually they work with vendors and distributors. I will also put BIG4 i.e. PwC, EY, KPMG and DL in this category as they usually provide more high-level consulting services such as security consulting, security/control review, IT governance and Penetration Testing.
4. End-user
These are the security teams who are looking after their own companies' IT security.
Among these 4 types, usually Type 2 and Type 3 are easier to get in. Type 1 mostly requires Singapore citizen. Type 4 usually want experienced staff and they always hunt people who has a couple of years of experience from Type 2 and Type 3 jobs.