New Shahamah is villa plots and family houses well out from the island, and plenty of those gardens have a hutch in a shaded corner. A rabbit that spends any time outdoors needs its coat and nails watched more closely, not less. Salonist lists the travelling groomers and small-pet clinics who cover the town, with open diaries and reviews you can read first. The wider pet grooming options in New Shahamah page shows who takes rabbits.
A visit follows a steady order. The handler weighs the rabbit and looks at teeth, eyes and feet, then brushes the loose undercoat away in stages, unpicks knots with a comb and fingertips, snips the claws just clear of the pink, and finishes by checking the ears, the scent glands and the fur under the tail for muck. There is no bath, no dryer and no turning the rabbit onto its back. Half an hour is usual, a little longer for a woolly breed. Try rabbit grooming in Rowdhat Abu Dhabi (RAD) if you cannot get a slot.
Out here the rates are gentler than on the island. Claws on their own come in around AED 40 to 75, a full groom AED 90 to 160, and a serious de-mat AED 135 to 220, with mileage added for a home call. Compare rabbit grooming in SE 1 before deciding.
The single most important thing in a villa is where the hutch sits. Bring it indoors under cooling from spring onwards, since a rabbit in a garden shed can be in real trouble long before you notice, and keep the coat clean so flies get no chance to lay near the tail. Owners a little further out book rabbit grooming in SE 11 on the same basis.
Because no groomer works from New Shahamah itself, the platform puts you in touch with handlers who drive out and clinics within reach, and the list grows as new businesses sign up. Salonist carries 15,000+ businesses in 60 countries and more than 2 million reviews, so you can judge a groomer, take a time and settle up without a call. Also see rabbit grooming in SE 2.