Is this phrase correct?
The Contractor declares to have the exclusive right to authorise...
or should it be:
The Contractor declares that it has the exclusive right to authorise...
Your first sentence is grammatically correct. In your second one use 'impersonal IT' is wrong. Put 'he' instead. It would be nice. If by any chance you want to retain 'it' express it like this:
*The contractor declares that it is his exclusive right ...
Here 'it' is anaphoric in a pseudo cleft sentence. Pseudo cleft is the name given to a sentence which , otherwise straight forward, we cleave into two halves to lay intended stress on something. Your examples are case in point.
However if it refers to a company then the issue is different. There might have been no need of asking the question.