"Is there a connection between anarchist and globalist?"
To answer your question.
No. Anarchism means "no rulers".
It's Individual. It has nothing to do with a globalists agenda/policies.
Wikipedia
"Globalism is group of ideologies that advocate the concept of globalization. It tends to advocate for such policies as increases in immigration, free trade, lowering tariffs, interventionism and global governance."
You could say; This is statism in it's biggest form.
Edit; added
We can agree on that. Thanks for taking the time to educate me. Much appreciated!