Learn Hardcore Norwegian: I løpet av søknadsprosessen må hun gi samtykke til at de sjekker identiteten hennes. - During the application process she must give consent for them to check her identity.

I løpet av is a fixed prepositional expression meaning during / in the course of. It’s followed by a noun phrase in the definite form or with a determiner, e.g. i løpet av dagen, i løpet av søknadsprosessen. You generally don’t split it up or replace parts of it (not i løpet søknadsprosessen).

Why is it søknadsprosessen (definite form) and not søknadsprosess?

Norwegian often uses the definite form to refer to a specific, understood process: the application process → søknadsprosessen.
Form breakdown: søknad (application) + prosess (process) + -en (definite ending for masculine nouns) = søknadsprosessen.

What is the function of må in this sentence?

Må is a modal verb meaning must / has to. With modal verbs, Norwegian uses the infinitive of the main verb afterward (without å):
må gi = must give (not må å gi).

Why is it gi samtykke and not something like gi et samtykke?

Gi samtykke is a common collocation meaning to give consent. It’s often used without an article because it refers to consent as an abstract/legal concept. You can sometimes see gi et samtykke, but gi samtykke is the standard phrasing in administrative language.

Why does it say til at after samtykke?

Samtykke til means consent to. When what you consent to is an action expressed as a clause, Norwegian typically uses til at + clause:
gi samtykke til at ... = give consent for/that ...
If it’s just a noun phrase, you use til + noun: samtykke til kontroll (consent to a check).

Why is the verb in the subordinate clause sjekker (present tense), not an infinitive?

After at, you get a full clause with its own finite verb. Norwegian uses the present tense in many contexts where English might use an infinitive or a different tense:
til at de sjekker ... = for them to check ... / that they check ...
It’s normal Norwegian clause structure: subject + finite verb (de sjekker).

Is the word order different after at?

Yes. At introduces a subordinate clause, and in subordinate clauses Norwegian typically places sentence adverbs like ikke, aldri, ofte before the verb:

Main clause: De sjekker ikke identiteten.
Subordinate clause: ... at de ikke sjekker identiteten.
In your sentence there’s no such adverb, so the word order looks the same as English: de sjekker identiteten hennes.

Who does de refer to here? Is it like English they or an impersonal they?

It can be either depending on context. In administrative text, de often functions like an impersonal they meaning the authorities / the people handling the application / the organization. It doesn’t need an explicit antecedent in the sentence if it’s understood from context.

Why is it identiteten hennes and not hennes identitet?

Both are possible, but identiteten hennes is the most natural, neutral possessive pattern in Norwegian: noun (definite) + possessive.

identiteten hennes = her identity (common, neutral)
hennes identitet = her identity (more emphatic/formal or contrastive)

Why is identitet in the definite form (identiteten)?

Because Norwegian typically uses the definite form when a noun is specified/possessed: the identity (of her) → identiteten hennes. The possessive doesn’t replace the definite ending; it comes in addition to it in this common structure.

Could samtykke take for at instead of til at?

Not normally in this meaning. Samtykke selects til: samtykke til ....
For at usually means in order to or introduces a purpose clause, which doesn’t fit the structure gi samtykke the same way.

Is this sentence in present tense even though it refers to a requirement in the future?

Yes. Norwegian often uses the present tense for general rules, procedures, and scheduled/expected actions. Here it states a general requirement during the process: må gi samtykke is a rule, not a one-time past event.