extemporize

v. t. To do, make, or utter extempore or off-hand; to prepare in great haste, under urgent necessity, or with scanty or unsuitable materials; as, to extemporize a dinner, a costume, etc. [ 1913 Webster ]

Themistocles . . . was of all men the best able to extemporize the right thing to be done. Jowett (Thucyd. ). [ 1913 Webster ]

Pitt, of whom it was said that he could extemporize a Queen's speech Lord Campbell. [ 1913 Webster ]