Charles Ellicott Commentary 1 Kings 1:39

"And Zadok the priest took the horn of oil out of the Tent, and anointed Solomon. And they blew the trumpet; and all the people said, [Long] live king Solomon." — 1 Kings 1:39 (ASV)

A horn of oil out of the tabernacle.—The sacred oil, the making of which is described in Exodus 30:22-30, was to be used for anointing the Tabernacle itself, and the altars and vessels as well as the priests. It was this oil, no doubt, which was used in this case. The Tabernacle proper was still at Gibeon (see 2 Chronicles 1:3); but a tent or tabernacle had been set up in Zion over the ark (2 Chronicles 1:4), and the haste with which all was done would necessitate taking the oil from the nearer source, in spite of the fact that Abiathar presided in Zion, and Zadok only in Gibeon.