Appointing a private investigator is illegal in the UAE.
Even if you bring them from outside the country, it is against Article No 378 of UAE Criminal Law, which says that a prison sentence will be inflicted on any person who attacks the sanctity of an individual’s private or family life by committing any of the following acts without their consent, except in legally permitted cases: a) Eavesdropping or recording or transmitting by any system any conversation held at a particular place or via the phone. b) Picking up or transmitting by any system a person’s picture.
However, if you believe that someone has committed a crime, the law gives you an alternative option – you have the right to request that police investigate and collect evidence for you, as per Article No 30 of the UAE Criminal Procedures Law No 35 of 1992.
Source: http://www.thenational.ae – UAE legal Q&A