J'imagine qu'il s'agit de travail temporaire et que le collaborateur en question est destiné à effectuer plusieurs contrats. Il doit en avoir terminé au moins un pour qu'il soit possible d'en ajouter un supplémentaire, ce qui semble logique.

Le terme "contrat" n'est peut-être pas le plus utilisé ici, j'ai un doute, mais l'idée générale est là.

English term (edited): The worker must have a completed hire

The worker must have a completed hire = literally: the variable "worker XYZ" must have the attribute "hiring process" set to "completed", before you can start meddling with the attribute "jobs/allocated tasks"

when someone is offered employment (be it permanent or temporary), often the person starts working even before all the various formalities and/or checks are completed; that "transitional period" can be just few days or in some cases far longer.

"In this process you can add an additional job for an existing worker.
The worker must have a completed hire in order to complete this process.
An open job requisition is a prerequisite for completing this process.\"
=>
An open job requisition is a prerequisite for completing this process.
= there must must an internal [to the company] demand for a "job" that I would more understand as "tâches à accomplir" rather than "poste de travail"

if you want to give this required "job/tâches à accomplir" to someone already employed (in effect change the "job description" on that employee), you can do it only if the "hiring process" for that employee has been completed!

IOW this computerised HR system won't allow you to start changing the "job description" by adding new tasks/responsibilities to someone who just started and his/her HR record is still incomplete.

Pour alléger le paragraphe et éviter des tournures maladroites.
>>Afin de finaliser ce processus, XXX doit compléter/achever/satisfaire (entièrement) son processus d'embauche.<<

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Note added at 8 days (2017-01-12 18:28:01 GMT)
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P.S. Oui, j'ai supprimé ma réponse précédente parce qu'on a caché ma réponse au "peer comment" initial. Je voudrais ajouter que lorsque j'offre mon aide bénévole ici, ce sont mes propres idées, mes propositions e tmes réflexions personnelles que j'exprime. Je ne consulte pas de francophones ou d'autres locuteurs natifs avant de participer. Je n'ai pas malheureusment le temps ni le loisir de passer mes journées entières à discourir et à m'éterniser dans des discussions KudoZ. Je réfléchis très sérieusement avant de faire des suggestions.
Je pense qu'il ne faut pas aller au-delà du texte original ni compliquer inutilement.
Bonne soirée. ;))

English term (edited): the worker must have a completed hire

Whilst I'm quite prepared to bow to the inevitably superior knowledge of our FR native-speaking colleagues, I feel that this way of expressing it conveys the right notion with the correct emphasis, as might be found in a piece of software.

I don't think it would be taking too much of a liberty to add 'impérativement' here, as the 'must' here is clearly a mandatory requirement (for the software to work properly).

Using an impersonal construction avoids all the arguments about passive or active.

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Note added at 8 jours (2017-01-13 09:37:26 GMT)
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There is another important clue in the source text we perhaps shoudn't overlook — employers 'hire'; we can't really say that an employee 'completes a hire', since an employee 'is hired'.