Relinquish, as an office

• Fancy way to resign
• Lower or resign
• Send down
• Call it quits
• Withdraw from office
• Resign one's position

Douglas Harper's Etymology Dictionary Word definitions in Douglas Harper's Etymology Dictionary
1610s (figurative), 1640s (literal), from Latin demittere "to send down," from de- (see de- ) + mittere "to send" (see mission ).

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
Demit \De*mit"\, v. t. [imp. & p. p. Demitted ; p. pr. & vb. n. Demitting .] [L. demittere to send or bring down, to lower; de- + mittere to send. Cf. Demise .] To let fall; to depress. [R.] They [peacocks] demit and let fall the same [i. e., their train]. ...