Risk premium is the excess expected return of the market over that of the risk-free asset. (There is no "(expected) risk premium".)
It is a property of the expected returns of two assets. It is an indication of investor's willingness to bear risk. High risk premium means less risk-bearing capacity in the market, where market participants are in risk-off mode.
Risk premium is not a forecast of future returns of the risky asset.
In contrast, something like a P/E ratio (or Shiller's cyclically adjusted CA P/E) is designed to reflect future returns. High P/E means asset is over-priced and lower future returns.
Risk premium can go up when price of risky asset decreases and/or risk-free rate decreases. Both tend to occur when market perceives uncertainty and shifts from a risk-on to risk-off regime. For example, S&P500 price and US Treasury yield (risk-free rate) could go down as capital shift from risky equity to safe US government debt.
This is not restricted to equity markets. Credit spread in the corporate bond market is also a kind of risk premium, for credit risk instead of market risk. The higher perceived default risk of the issuer, the higher is the yield demanded by investors. Corporates whose debt has high yield (junk) rating are perceived to have higher credit risk than those who are low yield (investment grade).
During market uncertainty, credit spread widens.