DUBLIN — The leader of the Irish nationalist party Sinn Fein testified Monday in a Belfast court against his own brother, who faces criminal charges of raping his daughter — an alleged crime that Adams himself admitted he’d kept secret within the family.

Gerry Adams, a reputed longtime commander of the outlawed Irish Republican Army and party leader for 30 years, insisted under cross-examination that he didn’t delay telling police to preserve his own political career atop Irish republicanism....