Although most photographic records online are from Queensland (Bold Systems, iNaturalist, ALA), the ALA shows a record from Sydney. A moth in the Gelechioid family Blastobasidae.
Well spotted! The actual species name is hard to be certain of, as B. tanyptera is very similar (and perhaps others) and it has many more southern records. Ther are more of this species in "Unidentified moths group 1". Some specimens of both species are plainer grey/brown, without the whitish part. Females have more slender labial palpi than this male.