Meaning of “sign on” - Learner’s Dictionary

sign on

phrasal verb with sign uk us /saɪn/ verb [ I, T ]
START WORK

to sign a document saying that you will work for someone:

She's signed on with a temp agency.
NOT IN WORK UK

to sign a form at a government office to say that you do not have a job and that you want to receive money from the government

(Definition of “sign on” from the Cambridge Learner’s Dictionary © Cambridge University Press)