Why does he do it?

Plenty of people hate their jobs, but one tries to make a living at what one's best at. Callan's an ex-soldier, finds civvy-street impossible to adjust to, is very good at killing people and believes, in the end, that it's mostly necessary. No doubt James Bond would moan just as much, except that he's paid so much more...

"Duck, I says..."

IIRC, Callan's done time in prison, so would find it difficult to get a normal job, especially when Hunter's there in the background making damn sure he can't. Realistically, he hasn't anywhere else to go - and Hunter knows it.

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He does it because he has no choice. No choice at all.

Hunter spells it out for Callan in the first episode: "Do this job for me or I'll have you killed."

If Callan tries to leave the Section he immediately becomes a liability and a security risk. Hunter is willing to make use of Callan as a skilled operative, but Callan is expendable. If his skills are no longer at Hunter's disposal then Callan becomes a removeable nuisance. Hunter will then let Meres or some of his other killers off the leash. Callan knows full well that it would then only be a matter of time before one of Hunter's trained attack-dogs puts a bullet through his brain.

Work for Hunter or die. Brutal but persuasive.