it's not call racing license, it's called a competition
license.
apply from www.smsa.org.sg
basically loh, no requirements at all, you only need the license if
you're intending to take part in OFFICIAL races, whether locally or
overseas (johor included).
1st time membership fee is $70, 6 passport photos required.
they will give you 1 card, your so called "racing license", where
whenever you go take part in a race, they'll give you a chop,
muchiam go SSDC take prac like that 
the license oso got several classes one, muchiam 2b 2a 2 like that.
but for bikes i think only 1 class, cars got more. that time i go i
never ask clearly. but basically to upgrade, you just need to race
more often.
races are usually held at kallang or pasir gudang.