The present disclosure concerns a recombinant yeast host cell exhibiting higher stability and, in some embodiments, higher fermentation performance. The recombinant yeast host cell stability has a limited ability to express an hydrolase during its propagation phase. In return, this limits the cleavage of a yeast cellular component during or after propagation which may be detrimental to the stability and/or fermentation performances. The recombinant yeast host cell expresses a heterologous hydrolase under the control of a heterologous promoter (for limiting the expression of the heterologous hydrolase during propagation and favoring the expression of the heterologous hydrolase during fermentation).