In this paper, we propose a quality-of-service (QoS) constrained power and rate allocation scheme for spectrum sharing systems. In particular, we assume existence of secondary users, who are allowed to access the spectrum occupied by a primary user subject to satisfying interference-power limitations. Specifically, we assume that the successful operation of the primary user requires a minimum-rate to be supported by its channel for a certain percentage of time, and obtain an average interference-power constraint that is required to be fulfilled by the secondary user. Applying this limitation, we obtain the maximum arrival-rate supported by a Rayleigh block-fading channel subject to satisfying a given statistical delay QoS constraint. In this respect, we derive an optimal adaptation policy that maximizes the effective capacity of the channel, and provide closed-form expressions for the power allocation and the effective capacity. In addition, we obtain closed-form expressions for the expenditure-power that is required at the secondary transmitter to achieve the above-mentioned capacity metric.