Hyaluronic acid is a humectant: an ingredient used in skincare to help hold water. It appears in serums, creams and cleansers, so a dedicated serum is optional rather than essential.
A thoughtful approach
A simple way to use it is to apply a serum to clean, slightly damp skin, then follow with moisturizer. If your moisturizer already contains it and your skin feels comfortable, another layer may add little to your routine.
Make it your own
Formulas differ. If a product causes irritation, stop using it and check the full ingredient list rather than assuming one ingredient is responsible.
Further reading: American Academy of Dermatology.