Three men, aged 53, 38 and 20 years old from the St Brides area of Newport, have been arrested on suspicion of slavery and servitude offences, Gwent Police said.
Four other suspects remain in custody and are assisting officers with their enquiries after the granting of a further 24 hours in custody by a District Judge.
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His mother Princess Diana was killed in a car crash in Paris in 1997 when he was just 12 and his brother William was 15.
The 21-year-old, who was arrested on Sunday, also allegedly injured two other people in the attack in the German city of Reutlingen.
She was going to the aid of a family member who got out of the car in the middle of the park and was dragged away by a different tiger.