It's worth remembering that businesses who write 'golden handcuff' clauses into their employees' contracts often try to insert similar clauses into the contracts which they have with their clients, such as "I/We agree not to engage the services of any person formerly employed by The Company, in any role similar to that which they have performed for The Company, within six months of such a person leaving the employment of The Company".
Something like that might well be unenforceable in law but in can often be enough to deter their clients from taking on someone whom they previously received good service from through an agency.