The UAE legal system has more layers than most jurisdictions. Federal law, emirate-specific law, sector regulators, free-zone frameworks, and two financial free zones (DIFC and ADGM) operating under common law. Knowing which framework governs your contract is half the work of reading it.
Federal vs. emirate
Federal law applies UAE-wide. Emirate law applies within that emirate, and can be more specific (e.g., Dubai's tenancy law sits on top of federal property law). When the two conflict, federal law generally wins for matters constitutionally reserved to the federation; emirate law wins for local matters.
Free zones
Most UAE free zones operate under a hybrid: federal law for criminal and certain commercial matters, free-zone-specific rules for licensing and operations. Two exceptions: DIFC and ADGM operate under their own English-language common-law systems, with their own courts.
If your contract is governed by DIFC or ADGM law, the rest of UAE law is largely irrelevant. If it's governed by "the laws of the UAE", you're in the federal-plus-emirate zone.
Practical checklist
Read the governing-law clause first. Read the dispute resolution clause second (which court? which arbitration centre?). Together they tell you which legal system actually decides the contract — which is usually more important than the contract's substance.