If you are flying SQ … technically there is no arrivals lounge in SIN. However if you your trip to SYD is on the same ticket then the boarding pass for your SIN-SYD flight will allow you entrance into the lounge. By same ticket I mean that it looks like you are transiting in SIN and not stopping over.
If you are interlining then you might have to stop at the transfer desk to get your SQ boarding pass first.
The above assumes you are travelling in business or first. If not then you will need *A Gold status to get into the lounge.
Moderator …. This post will most likely be better suited in the Singapore Airlines thread.