Are you getting the headphone icon on the display when a pair of headphones are plugged into the headphone jack?
If not, then as you say the headphone jack is faulty and needs to be replaced. They cannot be repaired.
Here’s a link to the ifixit Moto G4 Earphone Jack Replacement guide which should be of some help.
Replacement headphone jacks are available online. Just search for Moto G4 headphone jack part to get results for suppliers.
Here’s a link to just one supplier. It is shown only to give you an idea of the cost of the part. There are others that may suit you better.
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