-Burçlar ve renkler arasında bağlantı 'kuruyorum'.
What is the verb here and what does it mean?

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It means a lot of things.

"I'm making a connection between the zodiac signs and colors."
Kurmak is "making" in this sentence. "Bağlantı kurmak" is often used together meaning "connecting/making a connection"

"Masayı *kurmama* yardım et." = Help me *set* the table up. — "Masayı kurmak" is used together

"Polis hırsıza tuzak *kurdu*." = The police *set* a trap for the burglar. — "Tuzak kurmak" same as well

these are the most common ones that I could remember