high-headed
/ˌhʌɪˈhɛdɪd/adjective
1Having a high top or head; specifically (of a tree) having a high crown of foliage.
2Proud, arrogant.
3Of a person or animal: holding the head high. Also of a gait, etc.: characterized by this posture.
Origin
Mid 16th century; earliest use found in Thomas Phaer (?1510–1560), translator and physician. Partly from high + headed.