That's strange because Privet normally grows in any soil, even if its poor. You could try cutting them back by half, sprinkle some general fertilizer round the base of the plants & then hoeing it in lightly. Give them a good watering afterwards & , hopefully, they should pick up & grow this year.

When you planted it, did you reduce its height by half (if bare root) or a third (if container plants)? If not, do as Balcony describes - this is to persuade more shoots from the base to get the hedge to thicken up.