After the death of his brother Berthold IV, he styled himself Duke of Teck, and thus founded the elder line of the Dukes of Teck, which existed until 1439.

He was a son of Duke Conrad I of Zähringen and his wife Clementia of Luxembourg-Namur.

When his brother Berthold IV died in 1186, he inherited the family possessions in the foothills of the Swabian Jura, including Teck Castle and the office of Cup-bearer of the Abbey of St. Gall and the area on the upper Neckar that went with this office.

A Duke "Adalbert of Teck" is also mentioned on 20 June 1192 in Schwäbisch Gmünd, on 4 (or 10) December 1193 in Gelnhausen and on 12 December 1193 at the court of Henry VI in Frankfurt, in a document of Count Egino IV of Urach about Bebenhausen Abbey, and by Bishop Diethelm of Constance in 1192.

When his brother Hugh, Duke of Ullenburg died, Adalbert inherited his possessions in the Ortenau and the Breisgau.