In an ideal world, the terms of all business dealings with customers and suppliers would be clearly set out in written contracts, using express and unambiguous terms. But in reality, we know that many arrangements, even key commercial partnerships, are founded on incomplete or out of date contracts, or even on the basis of oral agreements. Under UAE law, these oral arrangements can still be binding contracts, so should not be overlooked.
When it comes to exclusivity, historical dealings between parties, on unconnected matters perhaps, which have been based on standard terms which deal with exclusivity, could be implied into future contracts. Similarly, if parties have, by their course of dealing, previously dealt together exclusively, such exclusivity could be implied into the oral contract where the implication is that the relationship should continue in the same way.
It is also worth noting that if the arrangement in question is a registered commercial agency, the UAE Agency Law provides for automatic exclusivity of the agent.
Best practice is to commit all of your commercial dealings to paper, even if they are long-standing arrangements, to avoid expense of time, money and, potentially, relationships, through disputes with your business partners down the line.