extemporise
ɪkˈstɛmpərʌɪz
ɛkˈstɛmpərʌɪz
verb
compose or perform something such as music or a speech without preparation; improvise.
he extemporized at the piano
improvise,ad lib,play it by ear,think on one’s feet,make it up as one goes along,take it as it comes,busk it,wing it,do something off the cuff