The Succession Act 2006 (NSW) recognises de facto and other types of relationships when considering whether a person may be entitled to take from their intestate partner's estate, and does not require that you or your partner be married.
Depending on the circumstances, you may be entitled to some or all of your partner's estate. The circumstances include (but are not limited to) the length and nature of your relationship with your partner, your partner's family and other relationships, and when your partner passed away.
If you do have a claim or entitlement on some or all of your partner's estate, you may be entitled to apply to the Court for Letters of Administration over your partner's estate in order to have the power to find, take control of, and dispose of your partner's estate.
It may also be suitable to refer the matter to the NSW Trustee and Guardian to request that they apply for the Letters. The NSW Trustee and Guardian is empowered to seek to be appointed administrator of the estate by the Court, and dispose of the assets of the estate according to law.
Disclaimer: This advice is general and is not intended to be relied upon as advice for your specific situation and circumstances. In order to provide an advice taking into account the entirety of your unique circumstances, I would strongly recommend that you seek further professional legal advice.
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