Which forms of verb can I use here?
The client must ensure that accurate records be/are/will be kept.
I don't know why Google translate example uses "be" here.
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In "that" clauses, the subjunctive is used to express a demand, a recommendation,
something that you wish for, or a hypothetical rather than actual situation. It is used with verbs such as demand, insist, pray, recommend, suggest, and semantically related nouns/adjectives, e.g. essential, important, insistence, proposal, etc.
Ensure does not fit in this list. Indicative mood should normally follow ensure, which becomes obvious by simply googling it. The first hit is usually from Oxford Languages, and this is where I found your sentence. The definition goes as follows:
ensure: make certain that (something) will occur or be the case.
- e.g. The client must ensure that accurate records are kept.
Therefore, the grammatically correct variant is with the present of the indicative, not the subjunctive.
Note that ensure carries a future connotation already, so using the future tense after it would be redundant.
Now, that doesn't mean that some people will not use be instead of are in a sentence like this. Even Gngram found few instances of it, though present indicative is definitely preferred.
Some do overuse subjunctive in formal texts so as to sound official. There are differences of subjunctive use between countries (for example, BrE uses it less than Am E) and even regions. However, strictly speaking, the subjunctive (be) is grammatically inaccurate in this particular context.
If you read the sentence examples with "ensure that" given by WordHippo, you will find that most of them are in the present tense of the indicative mood (except for the cases when the main sentence is in the past; then a past tense is used).
e.g. The organisers of the protest now face a desperate rush over the next month to ensure that they are ready in time for the summit.