Exclusive rate or price can mean one of two things. It can be a price that does not contain tax nor any fees for something additional (like insurance coverage). For example, a price can be VAT-exclusive or VAT-inclusive. Exclusive rate can also refer to a special offer.
In car rental, exclusive rate is usually a rate type that includes only the base rental price for a set period with either limited or unlimited mileage. It usually does not include any kind of insurance coverage and it may also exclude mandatory taxes and fees. As a result, it is often referred to as “time & mileage”. Exclusive rate is most commonly used in North-America.