冀 is a bound morpheme (b.f.) in modern Chinese—it cannot stand alone as a free word. It appears only inside compounds or fixed contexts. Its main uses are: (1) in formal or literary writing as a verb root meaning 'to hope' or 'to long for' (e.g., 希冀, 冀望); (2) as the official one-character abbreviation for Hebei Province (seen on license plates, in postal codes, etc.). Because it's a bound form, you'll never use 冀 by itself in everyday speech.