How should I invest if I'm planning to move overseas in a year? Should I only wait till I've settled down at a spot?

Moving permanently or short-term? If permanently, maybe better to wait till settle down & invest from where you are going.

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If you are planning to return to Singapore, maybe start researching on which stock broker you want to use. Can do a walk in to one of the Investment centers to check if there are any limitations while you are overseas. I'm sure they can advise you without you having to sign up.

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If you just have spare cash that you won't be touching and don't want it to sit in the bank while you're away, and cannot be bothered to constantly monitor the market. Can consider SSB, STI EFT, or just a high interest fixed saving bond. You need a investment account for this. I'm not suggesting topping up your CPF as I'm assuming you want access to it when you return.

I think what might help is to open a brokerage that has presence in both sg & the place you are going to overseas. Then just invest as per normal.