This paper aims at designing both a nonstandard anti-windup action and an event-triggering mechanism that reduce the transmission activity on the network while preserving the asymptotic stability of a linear system under a dynamic output-feedback controller. The event-triggering policy is based on the use of an additional internal dynamic variable. The nonstandard antiwindup term, which uses the difference between the transmitted and the current control output, is added to the controller structure to further save the communication resources. Sufficient conditions in terms of matrix inequalities are proposed to compute the anti-windup gain and the triggering parameters while avoiding the Zeno behavior. Numerical algorithms with feasibility guarantees allow to reduce the amount of data transmissions. Through numerical examples, we illustrate the efficacy of the proposed approach.