Current and future wireless networks are expected to provide high data rates and increased bandwidth utilization. Spectrum sharing cognitive radio networks have been proposed to increase the spectrum efficiency where a secondary user (SU) coexists with a primary user (PU) as long the interference from the SU to the PU receiver (PU-Rx) is properly controlled. Thus, the SU transmission is limited due to the interference power constraint. To overcome the secondary system coverage limitation, cognitive cooperative relaying has been considered to improve the secondary system capacity. In this work, we analyze a cooperative automatic repeat request (ARQ) cognitive relay network where an SU transmitter (SU-Tx) communicates with an SU receiver (SU-Rx) with the help of a single secondary relay (SR) in the presence of a single primary link. The channels are assumed to be independent Rayleigh fading and perfectly known. In order to protect the primary system against harmful interference from the secondary system, a peak interference power constraint that the PU can tolerate is considered. In addition, the SU-Tx and SR are also limited by their maximum transmit power constraints. In particular, we evaluate the outage probability of the secondary network for non-cooperative and cooperative ARQ (C-ARQ). To minimize the outage probability, the SR will retransmit the message to the SU-Rx if the SU-Tx to SU-Rx link is in outage. For delay limited applications, the message retransmission is bounded by the maximum number of retransmissions. The outage probability for C-ARQ at the SU-Rx depends on the probability of the SR of being able to decode the message. The numerical results indicate that the secondary network outage probability of the C-ARQ significantly outperforms the Non-C-ARQ. Moreover, the secondary network performance is degraded when the channel mean powers of the interference links increase.