New Gears for Vintage bike?

Hi (first time poster)

I have a vintage 11 speed Peugeot bike and would like to give it some more gears so that it can get me up hills more easily as right now its a struggle. I'm pretty useless with mechanics and so would take it to my shop to get updated but I was wondering what all would need to be updated and what sort of a price it would cost me?

Thanks