Extemporize
Extemporize , intransitive verb
To speak extempore; especially, to discourse without special preparation; to make an offhand address.
Extemporize , transitive verb
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.
Themistocles... was of all men the best able to extemporize the right thing to be done.
Pitt, of whom it was said that he could extemporize a Queen's speech