extemporize
US /ɪkˈstem.pə.raɪz/
UK /ɪkˈstem.pə.raɪz/

1.
to compose, perform, or utter something without preparation; improvise
:
•
The jazz musician could extemporize a solo on the spot.
•
She had to extemporize a speech when the main speaker didn't show up.