Is a wife who is patient when her husband takes another wife rewarded?

Yes — patience in trials, including feelings of jealousy and sadness, is promised reward by Allah. Allah says that the patient are given their reward without measure, and the Prophet ﷺ said that no hardship or sorrow befalls a Muslim but that Allah expiates his sins through it. Patience does not mean swallowing injustice in silence; a wife can still claim her rights and remind kindly. Patience is guarding your tongue, actions and faith when your heart is hurting. If there is injustice, seeking justice is also an act of worship. See counselling.