Robust clustered standard errors can change your standard errors in both directions. That is, clustered standard errors can be larger or smaller than conventional standard errors. The direction in which standard errors will change depends on the sign of the intra-class correlation. The following post explains robust standard errors in greater detail:

https://economictheoryblog.com/2016/09/25/clustered-standard-errors/

Robust clustered standard errors can change your standard errors in both directions. That is, clustered standard errors can be larger or smaller than conventional standard errors. The direction in which standard errors will change depends on the sign of the intra-class correlation. This post explains robust standard errors in greater detail.