I don't think you need government clearance, but you could always contact them and ask.
http://nationalzoo.si.edu/Education/WildlifeCareers/
Working in a Zoo
The qualifications for employment in a zoo depend on the job. If you are interested in a profession working in close contact with animals on a daily basis, such as wildlife biologist or veterinarian, an advanced degree in zoology or veterinary medicine is required. Jobs requiring less schooling but include frequent, direct contact with animals include veterinary technician, zoo keeper, or wildlife technician. For all positions, a commitment to the welfare of animals and conservation of species is critical. Learn about staff at the National Zoo.
Since most of these jobs are popular, there are often more applicants than positions. You should expect strong competition and salaries considered low relative to the level of education necessary to perform them. And these jobs aren't easy. Caring for animals can require around-the-clock attention in some settings. Wildlife biology can involve working outdoors in sometimes difficult field environments.
http://nationalzoo.si.edu/AboutUs/Staff/Interviews/PerryLaurie.cfm
What was your career path that led you to the job you do today?
I have always known that I wanted to work with animals. As a child, I wanted to become a marine biologist and work with whales/dolphins. In college, I became interested in primates (especially apes). I have a degree in Biological Sciences (with a zoology concentration) from the University of Maryland. While going to school, I volunteered at the zoo as a keeper aide in the ape house. When I graduated, I was hired as a keeper.
http://nationalzoo.si.edu/Audiences/JobSeekers/
Get experience with animals. There's a list below of some ideas. Before and/or during college see if you can volunteer at a zoo. A lot of zoos offer summer camps, volunteer opportunities, and internships. There are also a couple colleges that have a teaching zoo, so you can get experience as well as an education.
Though you may not need a degree, depending on the zoo you apply to, you should at least get an associate's (2 yrs). Though a bachelor's (4 yrs) or higher would be better.
After you get your degree it still might be hard to get a job right away. You might need to do an internship and/or work some other job (at the zoo or somewhere else) till a position opens up.
Some Degrees:
Zoo/Zookeeping/Animal Technology
Animal/Zoo/Wildlife Management and/or Training
Animal/Zoo/Aquarium Science
Zoology
Zoo Education
Animal/Zoo/Wildlife Care and/or Husbandry
Zoo/Exotic/Wildlife Conservation
Ethology or Animal Behavior
Here's some more links. I hope this helps. GOOD LUCK.
http://www.sandiegozoo.org/jobs/keeper_faq.html
How do I become an animal keeper?
There is no single way to become a keeper, but the more education and hands-on experience you have, the better.
Education– While you’re in school, learn as much as you can in your science classes. In college, choose a degree program in animal-related fields like biology, zoology, botany, ecology, conservation science, or animal behavior. Take as many different courses in those areas as you can, and graduate with a Bachelor’s degree in your chosen field. (Here’s a BIG hint: the competition for jobs caring for animals is so strong that you really HAVE to have a college degree these days to be considered.)
Hands-on Experience– Find opportunities to work with animals. Some potential keepers have volunteered at our department of Conservation and Research for Endangered Species (CRES), assisting CRES scientists and technicians. Sometimes work-study opportunities are available for college students.
What are some other ways to gain animal experience?
Some places to look for volunteer jobs or internships might be:
• Veterinary offices
• Animal training classes (does your dog need obedience training?)
• Local Humane Society
• Local Park Service
• Wildlife rehabilitation centers (like for wolves, bears, big cats, birds of prey, and even bats)
• Animal shelters
• Farms (for domestic animals, or even ostrich, llama, or butterfly farms)
• Pet breeders (those that breed specific kinds of dogs, cats, or horses)
• Horse stables and boarding facilities
• 4-H Clubs
http://www.seaworld.org/career-resources/info-books/zoo-careers/starting-zoological-career.htm
http://www.aza.org/ForEveryone/Careers/
Requirements
The conservation and scientific programs in zoos and aquariums have become highly technical and specialized. Although practical experience with animals may sometimes be substituted for academic training, most entry-level keeper positions now require a four-year college degree. Training in animal science, zoology, marine biology, conservation biology, wildlife management, and animal behavior is preferred. Curatorial, research, and conservation positions typically require advanced academic degrees.
Students wishing to pursue animal-related careers are encouraged to carefully review the curriculum of the schools they wish to attend, as some programs focus more on a zoological application than others. Students who are interested in the business side of zoo and aquarium operations should concentrate on skills related to a particular area of expertise, such as accounting, public relations, marketing, personnel management, etc. Whatever your career goal, guidance counselors can offer assistance in determining the most appropriate course of study.
http://www.wonderferret.com/zooed/keeper-jobs.html
Improving Your Chances of Getting a Keeper Job
Courtesy of A.A.Z.K.
Although most zoos will be looking for experienced and academically able staff you can improve your chances by amassing various other skills. If you already have keeping experience then so much the better, however the following will be a big help.
(a) Learn to drive a....
http://aazk.org/zoo_career.php
http://www.stlzoo.org/animals/soyouwanttobeazookeeper/
http://www.nczoo.org/becomingakeeper/
http://www.princetonreview.com/Careers.aspx?cid=166&uidbadge=%07
http://www.schoolsintheusa.com/careerprofiles_details.cfm?carId=1456
School:
http://www.wonderferret.com/zooed/
http://www.seaworld.org/career-resources/info-books/zoo-careers/school-&-university-programs.htm
http://www.moorparkcollege.edu/current_students/teaching_zoo/other_programs.shtml
http://inst.sfcc.edu/~zoo/PROGINFO.HTM
http://www.moorparkcollege.edu/current_students/teaching_zoo/FAQs.shtml
http://www.thefutureschannel.com/dockets/realworld/teaching_zoo/
http://www.amazon.com/Kicked-Bitten-Scratched-Lessons-Trainers/dp/0670037680
http://animalscience.calpoly.edu/areas_of_study/zoo/index.asp
some internships/volunteer opportunities:
http://www.aza.org/JobListings/index.cfm?Keywords=Keeper&Filter=Internships
http://www.aazk.org/job_listings.php
http://nationalzoo.si.edu/Support/Volunteer/default.cfm
http://www.sandiegozoo.org/jobs/general_info.html
http://www.indyzoo.com/content.aspx?cid=272
http://www.houstonzoo.org/intern/
http://www.cmzoo.org/getInvolved/volunteer/opportunities.asp
http://www.denverzoo.org/involved/career.asp
http://www.dallaszoo.com/subnav/volunteer/Vol_2_aquarium.htm
http://www.redriverzoo.org/internships/animalkeeper.epl
http://www.brookfieldzoo.org/pagegen/inc/InternshipApplication2006.pdf
http://www.fortworthzoo.com/about/job.php?id=91
http://www.rollinghillswildlife.com/vol_web/admin/birminghamzoo_intern-college-program3.pdf
http://www.bigcatrescue.org/volunteer.htm
http://disney.go.com/disneycareers/internships/wdw/students/roles/animal_programs/animal_programs.html
http://disney.go.com/disneycareers/wdwcareers/internship/animal_programs.html#animal_behavior
https://disney.recruitmax.com//main/careerportal/default.cfm
Market Title - Animal Programs/