David reigned as king of Israel for 40 years. The first seven and a half years, he reigned from Hebron, and the remainder of the years he ruled from Jerusalem.

And the time that David was king in Hebron over the house of Judah was seven years and six months (2 Samuel 2.11). 

Is that significant or does it symbolize anything? Not that I can tell. Yes, we know that the Lord had made David king. If the Lord had a symbolic reason for having David spend the first seven years in Hebron, I have not found it.