A "local embassy" refers to a diplomatic office or consulate established by one country in another country to represent its interests and provide services to its citizens who are living or traveling in that country. Full definition
For western governments, «They basically have people from the local embassies go, they don't send the high - level delegations. (qz.com)
The U.S. has announced that it is preparing to send 150 Marines into South Sudan, to help evacuate American citizens and protect the local embassy... (relevantmagazine.com)
If you're travelling and doing anything other than building sandcastles on the beach, the local embassy needs to know. (theguardian.com)