This paper addresses the problem of opportunistic spectrum access in support of mission-critical ultra-reliable and low latency communications (URLLC). Considering the ability of supporting short packet transmissions in URLLC scenarios, a new capacity metric in finite blocklength regime is introduced as the traditional performance metrics such as ergodic capacity and outage capacity are no longer applicable. We focus on an opportunistic spectrum access system in which the secondary user (SU) opportunistically occupies the frequency resources of the primary user (PU) and transmits reliable short packets to its destination. An achievable rate maximization problem is then formulated for the SU in supporting URLLC services, subject to a probabilistic received-power constraint at the PU receiver and imperfect channel knowledge of the SU-PU link. To tackle this problem, an optimal power allocation policy is proposed. Closed-form expressions are then derived for the maximum achievable rate in finite blocklength regime, the approximate transmission rate at high signal-to-noise ratios (SNRs) and the optimal average power. Numerical results validate the accuracy of the proposed closed-form expressions and further reveal the impact of channel estimation error, block error probability, finite blocklength and received-power constraint.