Yes, if they are employed by the agency specifically to work at your school, which is usually the case for most school kitchen staff but not necessarily for cleaning staff. Cleaning staff wouldn't be eligible if the cleaning contractor employs them to move around from one school to another as required, one week cleaning your school, one week somewhere else. The legal definition in the Regulations of eligibility to be a Staff Governor is "persons who are paid to work at the school" at the time when they are elected. The same definition applies in deciding who can vote for Staff Governors. The legal definition doesn't retrict eligibility to people who are directly employed by you, the test is whether they are "paid to work at" your school (irrespective of who is paying them to do the work), so visiting music teachers etc wouldn't qualify.