The problem of state observation is addressed for a class of systems subject to sensor delay and parameter uncertainty. The unknown parameter vector enter a finite-dimensional state equation through a possibly output-dependent regressor. The sensor delay effect is captured by a first-order hyperbolic PDE. Doing so, the system turns out to be an ODE-PDE association with a connection point not accessible to measurements. An adaptive observer is constructed by combining ideas from PDE-based and ODE-based design approaches. The observer provides estimates of the ODE subsystem states and parameters, on the one hand, and of the sensor states, on the other. Observer exponential convergence is established under an ad-hoc persistent excitation condition involving the regressor.