Η αρμόδια αρχή εγκρίνει έκδοση υπό την προϋπόθεση ότι δόθηκε φωτογραφία.

Because it agrees with αρχή, which is a feminine noun.

In Greek, adjectives usually match the noun they describe in:

• gender
• number
• case

So here:

• η αρχή = feminine singular nominative
• αρμόδια must also be feminine singular nominative

That is why you get η αρμόδια αρχή.

Αρχή is in the nominative singular, because it is the subject of εγκρίνει.

You can tell from both meaning and structure:

• Η αρμόδια αρχή is the thing doing the approving
• the verb εγκρίνει is third person singular, matching that singular subject

So the basic structure is:

• Η αρμόδια αρχή = subject
• εγκρίνει = verb
• έκδοση = object

Greek often leaves out the article in formal, administrative, and legal style, especially with abstract or institutional nouns.

So εγκρίνει έκδοση is a formal way of saying something like:

• approves issuance
• approves the issuing / the issuance

If you said εγκρίνει την έκδοση, that would sound more explicitly definite, like a specific issuance already understood from context.

Both are possible, but the version without the article is very common in bureaucratic Greek.

Because some feminine nouns have the same form in nominative and accusative singular.

Έκδοση is one of those nouns:

• nominative: η έκδοση
• accusative: την έκδοση

Without the article, the bare form is just έκδοση in both cases, so you identify the case from the sentence structure.

Here it is the direct object of εγκρίνει, so it is accusative.

It is a fixed formal expression meaning:

• on the condition that
• provided that
• under the condition that

It is very common in official and legal Greek.

You can think of it as:

• υπό = under
• την προϋπόθεση = the condition / prerequisite
• ότι = that

But in practice, it is best learned as one chunk: υπό την προϋπόθεση ότι.

Ότι introduces a subordinate clause.

Here it introduces the condition that must be met:

• δόθηκε φωτογραφία

So the structure is:

• main clause: Η αρμόδια αρχή εγκρίνει έκδοση
• subordinate clause: υπό την προϋπόθεση ότι δόθηκε φωτογραφία

In English, this is similar to that after expressions like on condition that or provided that.

Δόθηκε is the aorist passive indicative, third person singular of δίνω.

So grammatically it means:

• was given

In this kind of context, English may translate it more naturally as:

• was provided
• was submitted

A few useful related forms:

• δίνω = I give
• έδωσε = he/she/it gave
• δόθηκε = it was given

Because δόθηκε is passive.

In a passive sentence, the thing receiving the action in English-style active logic becomes the grammatical subject.

So:

• active idea: someone gave a photograph
• passive Greek here: a photograph was given

That makes φωτογραφία the subject of δόθηκε.

Also, it appears without an article, which gives it an indefinite sense:

• a photograph rather than
• the photograph

This is very common in formal Greek.

• εγκρίνει is in the present tense because official or legal language often uses the present to state a general rule or standing procedure.
• δόθηκε is in the aorist because it refers to a completed action that must already have happened for the condition to be satisfied.

So the sentence is basically saying:

• as a general rule, the authority approves issuance
• but only if the photo has already been provided

No, Greek word order is fairly flexible.

This sentence uses a very natural and formal order:

• Η αρμόδια αρχή
• εγκρίνει
• έκδοση
• υπό την προϋπόθεση ότι...

That order is clear and neutral for official language.

Greek could rearrange parts for emphasis, but this version is the most straightforward for a bureaucratic statement.

Because several features are typical of administrative/legal Greek:

• αρμόδια αρχή = a standard official phrase
• εγκρίνει έκδοση = compact bureaucratic wording
• υπό την προϋπόθεση ότι = highly formal connector
• omission of some articles where English might expect them

This style is normal in regulations, forms, government decisions, and legal documents, but it is less common in everyday conversation.

In everyday Greek, someone might express the same idea in a simpler and less official way.