The perfecting of an appeal shall not stay enforcement of the judgment or order of the trial court awarding attorney’s fees or costs, or both, if the judgment or order appealed from was rendered in a proceeding under the Family Code, unless an undertaking is given in a sum and upon conditions fixed by the trial court.
Source:
Section 917.75, https://leginfo.legislature.ca.gov/faces/codes_displaySection.xhtml?lawCode=CCP§ionNum=917.75..