You can replace the headphone jack, your challenge will be the soldering and locating the part. If you have a hot air station, you could replace it fairly easily. It's also possible with a good soldering iron, flux, and a solder sucker or wick.
If you're comfortable with the soldering part, you still need to locate the part. You can either look on aliexpress, as they have some headphone jacks listed for the XPS 13, or you could look on eBay for a XPS 13 motherboard thats broken, and transfer the headphone jack from that board.