Wiktionary
vb. (context idiomatic English) To motivate or encourage (someone) to start sooner or move faster.
Usage examples of "light a fire under".
Missy accepted, hoping to light a fire under Bony, but she only managed to push him farther away.
Her way of giving was to push the people she cared about, to light a fire under them.
But how could she light a fire under someone who didn't want to be lit?
I'm pretty sure Site Services can rustle up a bed by quitting time, if I light a fire under them.
We don't want to wait for the gnomes to light a fire under the pot.
If we're going to announce the existence of Shannon's little project, then I'd better sit down with Arnaud Marquette and light a fire under my planning staff.
He would have to light a fire under Omerna, put the fear of the Light into him.
Nothing like an in-person, face-to-face appeal, I always say, to light a fire under people.