Beta is also applied to a given security, not just a portfolio (which can be done in aggregate) or a money manager perforamance.
Each security's price movement is correlated to the wider market (usually the S&P 500) and has a beta coefficient that represents approximately how it behaves relative to the index, e.g., the SPY would have a beta of 1 because it moves in lock step with the SP500.
Portfolio beta would be approximated by volume weighting the individual security betas in the portfolio.