The aim of this paper is to exploit cognitive-ratio inspired NOMA (CR-NOMA) transmission to reduce the age of information in wireless networks. In particular, two CR-NOMA transmission protocols are developed by utilizing the key features of different data generation models and applying CR-NOMA as an add-on to a legacy orthogonal multiple access (OMA) based network. The fact that the implementation of CR-NOMA causes little disruption to the legacy OMA network means that the proposed CR-NOMA protocols can be practically implemented in various communication systems which are based on OMA. Closed-form expressions for the AoI achieved by the proposed NOMA protocols are developed to facilitate performance evaluation, and asymptotic studies are carried out to identify two benefits of using NOMA to reduce the AoI in wireless networks. One is that the use of NOMA provides users more opportunities to transmit, which means that the users can update their base station more frequently. The other is that the use of NOMA can reduce access delay, i.e., the users are scheduled to transmit earlier than in the OMA case, which is useful to improve the freshness of the data available in the wireless network.