The king of the Ammonites sought to take Jabesh Gilead,
Then the elders of Jabesh said to him, “Hold off for seven days, that we may send messengers to all the territory of Israel. And then, if there is no one to save us, we will come out to you” (1 Samuel 11.3).
The king granted their request, but in so doing he set up his own defeat, because when Saul, the new king of Israel, heard of this, he immediately when to the defense of Jabesh Gilead and saved them.
The elders of Jabesh Gilead asked for a seven day waiting period to find out whether anyone would come to their aid. Why did they say seven days? Perhaps they figured that was enough time for messengers to travel anywhere in the land of Israel, and then for the messengers to return.
Other than that, we cannot see any significance to the use of “seven” in this passage.