May certain conditions be placed upon the exercise of a license?

Yes. ABC, at the request of the applicant or licensee, may restrict the hours of sale, advertising, entertainment, or any condition that appears to alleviate objections to the premises operation. Such conditions have been imposed restricting licensed operations in the vicinity of churches, schools, and residential areas. Also, conditions relating to the personal qualifications of the applicant or licensee may be endorsed upon the license. (Sections 23800-23805 and Rules 61.3-61.4)

A licensee may petition for the removal or modification of a condition. The fee for the petition is $100. By law, ABC must notify the local governing body of any petition to remove or modify conditions. the local governing body has 30 days in which to object to the modification or removal. A hearing is then held if the local government objects.

When conditions have been imposed on a license, where otherwise the license would be denied, for reasons relating to the premises, no petition for removal of the conditions may be filed within one year from the date the license was issued, or from the date a similar petition was denied. However, ABC may, at its discretion, accept a petition to remove conditions, if the reasons which caused the imposition of conditions no longer exists. (Section 23803 and Rule 66)

Source: https://www.abc.ca.gov/questions/licenses