For the first time last night I was playing a game where me civ spanned more than one continent. I noticed that none of the new cities on the 2nd continent had the trade arrow symbol.

Is there a tech or city improvement needed to connect these cities back to the capital?

I believe lighthouses enable trading across the sea, not 100 % sure though.

I'll double check tonight when I get home, but I'm 99.9% sure all cities in question, including the capital, have lighthouses....

Sailing allows trade routes across coastal squares. Astronomy allows trade routes across ocean squares. No city improvements are needed.