Asker, it's very hard to help you properly, as you don't give the full context.

Normally, if the 'business partner' were a person, one migh say 'associé' — the 'business' being usually implicit. But I get the impression this is probably not the ase here, as it sounds like this may be a partnership between businesses; in fact, these days, 'partner' is often just a fashionable synonym for 'supplier'!
Assuming this is the case, then my suggestion might well fit; note, of course, that it literally translates 'partner business', but if that is the kind of sense in which it is being used here, then that is of no consequence — the two are synonyms.
Of course, in very many contexts, simply 'partenaire' is all that is needed — we know we are in a business context

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Note added at 5 hrs (2019-03-17 10:40:11 GMT)
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If this is a business talking, then it is fairly implicit that there partner is going to be for doing business (i.e. 'a partner in business').
However, it is not a given that they are necessarily going to be another business (cf. things like PPP etc.) — so I am understanding this with the connotation of 'business that is our partner', although that's only one aspect that comes along to 'colour' the overall interpretation; in other words, I think the key issue here with 'business partner' is to contrast it with, say, 'private partner', 'institutional partner', etc.

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Note added at 6 hrs (2019-03-17 11:19:04 GMT)
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Do note there's nothing whatever in the source text to suggest this is a 'trading partner' — which seems unlikely, given the only context we know, which is HR.

Partenaire d'affaires en ressources humaines. Ou peut-être consultant s'il s'agit d'une personne pigiste en ressources humaines?