Relative to a standard linear regression, how would we expect the inclusion of a random intercept for cluster to change the parameter estimates on covariates in a model (if at all)?

Suppose I am regressing birthweight on mother’s age, and I have data for multiple births for (some) mothers. So mother’s age can vary both within mothers and between mothers. In my initial regression I fail to include a random intercept for mother. In my second model I include a random intercept for mother.

I know this will change the standard error of the coefficient on mother’s age, but will it change the actual estimate of the effect of mother’s age?

If I included a fixed effect for mother, I know this would now force the interpretation of the effect of mother’s age to be purely within-mother (because I’m “controlling for mother”). But I don’t think this is the case if I include a random effect for mother—but I’m not sure how the random effect changes the interpretation of the coefficient on mother’s age, if at all.