to extract, draw out, to extort, wheedle out of someone
Tu vas le flatter et lui soutirer autant d'or que tu peux.
You’re going to flatter him and get as much gold out of him as you can.
— Le Voyage de Chihiro (2001)
Comme ils sont riches, leur soutirer de l'argent ne leur manquerait pas.
Since they’re rich, they wouldn’t miss the money if we took it from them.
— Lady Vengeance (2005)
Ils ont essayé de me soutirer plus d'argent.
They tried to extort more money from me.