George Freeman was a Sydney bookmaker who had connections to the Chicago Outfit through Joseph Dan Testa. Same goes for Lennie McPherson. Back in the days LE even called these guys the "Australian contacts of the American Mafia" but I don't really know how much actual truth that statement holds.

After that era it seems there aren't really a lot of North America to Australia connections regarding organized crime. There are however plenty of connections to Europe.

Organized crime in Australia (and New Zealand) these days sees the involvement of a few major groups: Ndrangheta, outlaw motorcycle groups, Lebanese, Assyrians, Pacific Islanders and Vietnamese. Every now and then Chinese organized crime (mostly in New Zealand) and Albanian organized crime (there was an Albanian group active in Adelaide for some time) makes the news, but generally speaking it's not as pervasive.

There are Ndrangheta cells active in Sydney and Melbourne and there used to be one active in Perth as well. They're part of major clans and they absolutely have contacts throughout Italy and the rest of Europe. These are large international networks.

Outlaw motorcycle groups are arguably the biggest criminal factor in Australia. They have contacts with Italian organized crime regarding drug shipments; in 2014 for instance there were talks of a shipment of 51 million xtc pills to be send by an Italian clan based in Belgium to Australia, which was to be distributed by bikers. All the big outlaw motorcycle clubs are active in Australia, like the HA's. Membership of the big known clubs are mostly local Aussies.
Australia also has plenty of homegrown outlaw motorcycle clubs. Rebels MC are well known for instance, and they're a club with many members of Maltese origin. Even got a chapter in Malta and Maltese criminals also have plenty of Italian organized crime contacts so that's how they stay connected as well.
NZ also has homegrown clubs, of which the Head Hunters are the biggest in status.

Lebanese OC in Australia are local crime families that are based their neighborhoods in Sydney and Melbourne. Most of these families have a Sunni background with roots in Tripoli, but there are also Maronite Christian crime families active.
There are Lebanese crime families active in for instance Germany and Sweden, but these families mostly have a Mardelli/Mhallami background or a Shi'ite background so I don't think they are in contact with the Lebanese criminals in Australia seeing these are completely different clans. In Montreal however the Lebanese crime families are from a Maronite Christian background, but I haven't heard of them getting into contact with their Australian counterparts but it's possible.

Assyrian OC is also local in Australia, mostly in Sydney's southwest. There's Assyrian OC in Europe (mostly in Sweden) and in the USA as well (Detroit and San Diego) but I haven't heard of them getting into contact with their brethren in Australia.

Regarding Vietnamese OC on the other hand I did hear about Vietnamese criminals based in Australia getting into contact with Vietnamese criminals based in the UK. These days Vietnamese criminals mostly operate illegal marihuana grow houses and traffic in counterfeit goods and they do have cross-border networks (even if it's just for sharing know-how).

Samoan and Tongan gangs are mostly organized street gangs and their biggest presence is in New Zealand, but I did read about Samoan and Tongan gang members in NZ getting into touch with their counterparts in the USA. Both the USA as well as the Oceanic countries are deporting criminals back to Samoa and Tonga so I guess that's where they get to know each other. These contacts seem to involve the meth and the guns trade. Pacific gangs in Australia and NZ work a lot with bikers, as do the Lebanese gangs.

Chinese OC mostly involves representatives of known Triad groups and Albanian OC are also large clans that stay into contact with other clan members throughout Europe. These are large international networks. Russians are supposed to have a presence as well, but I think the Russian OC activity mostly involves money laundering.