After Saul became king, Samuel spoke by the word of the Lord to Saul that he should go to Gilgal and wait seven days, then Samuel would offer a sacrifice,
“You shall go down before me to Gilgal; and surely I will come down to you to offer burnt offerings and make sacrifices of peace offerings. Seven days you shall wait, till I come to you and show you what you should do.” (1 Samuel 10.8).
Why was Saul to wait seven days? The Bible does not say. However, Samuel gave these directions by the word of the Lord. Therefore, the Lord had something in mind, although He did not reveal it to us.
Sevens in the Bible 
and saul waited 7 days and samuel didnt show
Yes, that is true.
God was testing Saul in order for Saul and the people to see that Godly leadership requires total commitment, and God had warned the people that having a king would subject them to fragile leadership.
Saul proves this by being impatient and not willing to wait as instructed by God’s preacher.
Thanks for your insight.