Neighbour makes noise late at night, what are my legal options?

Went through this. Escalate in order, document everything. First, keep a log with dates, times and short recordings of the noise, you'll need evidence for any formal step. Second, report to your Town Council and involve your HDB grassroots, they can send a warning and mediate. Third, go to the Community Mediation Centre (CMC), it's low-cost and often works because a neutral party is involved. If all that fails, the Community Disputes Resolution Tribunals (CDRT) is the legal avenue, you can file a claim for unreasonable interference with your enjoyment of your home, and the court can order them to stop and even pay damages. There's also a newer Community Disputes framework being strengthened. Realistically mediation resolves most cases, courts are the last resort. Whatever you do, don't retaliate with your own noise, that weakens your case and can land you in trouble too.