E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Sport a Door or Oak.
To keep an outer door shut. In the Universities the College rooms have two doors, an outer and an inner one. The outer door is called the sporting door, and is opened with a key. When shut it is to give notice to visitors that the person who occupies the rooms is not at home, or is not to be disturbed. The word sport means to exhibit to the public, as, to sport a new equipage, to sport a new tile [hat], etc.; whence to have a new thing, as to sport an ægro-tat [sick-leave]; or merely to show to the public, as sport a door or oak. The word is a contraction of support. (French, supporter, to sustain, carry; Latin, supporto.)