How can a foreigner find a job in HR in Singapore?
I'm sorry but you are in for a tough time. Of all our country's manpower issues, HR is not where we are lacking. You have literally a throng of Singaporeans (both fresh grads and experienced) to compete against for the role of HR.
Salary is always a factor when considering candidate, so it depends on what nationality you are. How much a company is willing to pay also depends on its financial ability, job role and scope of work. But unless you are a Malaysian, chances are a Singaporean is going to be as affordable if not more affordable than you are, minus the paperwork and etc. needed to apply for your employment pass. S Pass isn't even as cheap as it looks, as it involves levies, insurance and whatnot.
So you might want to consider going for the companies that are likely to have a bigger salary budget and expanded job role, and show in your application and resume how you fit in and how your skill sets can contribute to the organisation. That will make you look more worthwhile and attractive as a candidate. Or you can work with recruitment agencies; they might be able to help you out as they have hiring customers.
Having lived in Singapore, you must be pretty aware that HR jobs are difficult to find in Singapore. The cost of living is also high; so you must also get a decent salary to keep you motivated. When you get married, the expenses are bound to go up.
If you have some savings and your BF can support you, starting a Recruitment/Training Consultancy would be ideal. As a PR guy, he can canvass, make use of the contacts and with your varied experience, business is bound to pick up. Alternatively, you can identify a Consultancy and join them even for a meagre salary, get to know the intricacies of the business within few months or maximum 1 year and then start your own Consultancy.
Barring the initial hiccups, business is bound to grow and you can be your own boss. If required, you can also look around for some tie-up with Indian Consultancies.
Otherwise, both of you can look for opportunities to migrate to Australia where lot of opportunities exist for HR and PR.
Thanks for the A2A but I'd second May Leong's answer. However, you might need to reconsider positioning yourself for an L&D function.
In my experience, companies are either cutting or freezing headcount for training department during bad times like now. With lower training budgets and online learning, the career runway of a trainer or L&D manager is getting shorter over time. To me, an L&D manager is no different from any admin manager.
If you want to design, develop and deliver L&D solutions/interventions, you should be going for L&D consulting firms.
While getting a job in HR in Singapore isn't as difficult as you may think, but what you need to adapt is the local culture.