For on the job/operational training trainers may well be competent based on qualifications/experience. I would therefore have a register of trainers (with details of competency) or have training included in job descriptions of the people that do such specialized training.
I have seen train the trainer qualifications for members of staff that do regular other sorts of training such as Induction, Hygiene, Food Safety, Internal Audits etc. although I don't it is necessary if you have evidence of competency of the trainer and trainees after receiving the training.
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