In the mean-variance framework, the only way to get a higher expected return is to be exposed to a higher beta, and the more risk-averse an agent, the lower the beta of their portfolio (lending portfolios). However, could it be that a more risk-averse individual has a higher discount rate than a less risk-averse individual (i.e., the more risk-averse individual is less keen to provide financing for a particular venture). Or does the risk-return trade-off need to hold in all models that assume rationality and market efficiency (ie., higher expected returns are only achieved by higher risk exposure, given a certain level of aggregate risk aversion as in the mean-variance framework)?
The mean-variance framework is about optimal portfolio choice given the distribution(s) of asset prices/returns. On the other hand, the risk-return trade-off comes from an asset pricing model that produces the distribution(s). Therefore, the following is not quite right:
In the mean-variance framework, the only way to get a higher expected return is to be exposed to a higher beta.
This follows from the asset pricing model, not the optimization framework. Hypothetically, if the asset pricing model implied higher risk assets had lower expected returns, exposure to a higher beta would not lead to a higher expected return – whether we use mean-variance optimization or not.
However, could it be that a more risk-averse individual has a higher discount rate than a less risk-averse individual?
Risk aversion for a particular individual is characterized by their utility function, not the discount rate. The discount rate may characterize impatience, though. This is in the context of portfolio optimization, e.g. the mean-variance framework. Meanwhile, in an asset pricing model the discount rate characterizes the risk aversion of a representative individual in a market equilibrium.
Or does the risk-return trade-off need to hold in all models that assume rationality and market efficiency?
The trade-off is due to the asset pricing model. Hypothetically, we could introduce an asset pricing model where the trade-off goes the other way (higher risk brings about lower expected return) or there is not trade-off at all.