Whether equilibrium is characterized by market clearing or not depends on which equilibrating forces are free to operate in the labor market in question. In the standard labor market models, three fundamental equilibrating forces are postulated. First, firms are free to hire as many or as few workers as they want depending on wages and other conditions of employment. Second, workers are free within limits to move from one market to another or into and out of the workforce depending on wages and other conditions of employment. And third, the wage paid is free to rise or fall depending on supply and demand conditions. When all three of these equilibrating forces are free to move, the labor market is expected to clear in equilibrium. Wages and employment will therefore reflect supply and demand conditions.

Beyond these barriers to equilibration, which are ubiquitous, there are also settings in which one of the equilibrating forces, the wage rate, is not free to adjust. Wages may be set above the market-clearing level by a variety of institutional forces including minimum wages laws. When this happens, the predictable consequence is unemployment.

Moving beyond this...

Efficiency wage models recognize that a higher wage may increase worker productivity, because existing workers have greater incentives to work more efficiently because firms that pay higher wages attract a larger pool of applicants, from whom they can hire more selectively.
Human capital models recognize that workers' skills and productivity can be augmented through education and training.

Finally, a fundamental aspect of labor market economics is that labor markets do not operate in isolation. Wages and employment levels in one geographic area, occupation, or skill group are determined not just by conditions in that labor market but by conditions in other labor markets as well.

Abowd, John M., Francis Kramarz and David N. Margolis. (1999). "High Wage Workers and high Wage Firms." Econometrica, 67(2): p. 251-334.

Bontemps, Christian, Jean-Marc Robin and Gerard J. van den Berg. (1999). "An Empirical Equilibrium Job Search Model with Search on the Job and Heterogeneous Workers and Firms." International Economic Review, 40(4): p. 1039-1074.