We define partial cognitive relay channel as a two-transmitter, two-receiver interference channel with a relay node such that one of the transmitters is a cognitive transmitter. As a more feasible assumption we assume that the cognitive transmitter has non-causally access to a part of the other transmitter's encoded message. The cognitive radio transmitter transmits simultaneously over the same channel instead of waiting for an idle channel which is traditional for a cognitive radio. We calculate the achievable rate region for partial cognitive relay channel based on the combination of partial decode-compress and forward for the relay, rate-splitting and Gel'fand and Pinsker coding. Numerical evaluation of the region in the practical Gaussian case is performed. We show that by defining a proper cooperation strategy among the transmitters, equipping some of them with the cognition capability and exploiting the relay nodes, the effective bandwidth of each transmitter will enhance greatly.