Ala. Code § 45-51A-33.59

The council by ordinance may create, change, and abolish offices, departments, or agencies, other than the offices, departments, and agencies established by this part. The council by ordinance may assign additional functions or duties to offices, departments, or agencies established by this part, but may not discontinue or assign to any other office, department, or agency any function or duty assigned by this part to a particular office, department, or agency.