Passet utløper i juni, så jeg må håndtere det før jeg bestiller billetter.

Norwegian normally uses the definite form when talking about a specific, known thing. Passet means the passport (your passport).

• et pass = a passport (indefinite)
• passet = the passport (definite)
  The sentence assumes you and the listener both know which passport you mean.

utløper is the present tense of å utløpe = to expire / run out (become invalid). It’s commonly used for documents, deadlines, subscriptions, etc.
Example patterns:

• Passet utløper i juni. (The passport expires in June.)
• Visumet utløper snart. (The visa expires soon.)

Norwegian (like English) often uses the present tense for scheduled/known future events, especially with a time expression:

• Passet utløper i juni. = a fixed fact about the future
  You could also say kommer til å utløpe i juni, but that’s more like is going to expire and can sound a bit heavier or more predictive.

i juni means in June (at some point during June). If you want by June (no later than June), you’d use something like:

• innen juni = by June (before June starts)
• innen utgangen av juni = by the end of June

Here så functions like so/therefore and introduces a new main clause. Norwegian typically puts a comma between two main clauses when they’re linked like this:

• Passet utløper i juni, så jeg må …
  It’s similar to English “..., so I have to ...”.

Both can mean therefore/so, but they behave differently:

• ..., så jeg må ... (very common linking conjunction; straightforward)
• ..., derfor må jeg ... (adverb; often a bit more formal)

Also note word order:

• ..., så jeg må ... (normal main-clause order)
• ..., derfor må jeg ... (because derfor takes the first position, the verb comes next)

Because så here is a conjunction linking two main clauses, not an adverb meaning “then.” After this kind of så, you start a normal main clause: subject + verb → jeg må.
Compare:

• ..., så jeg må bestille... = so I must order...
• Så må jeg bestille... = then I must order... (så = “then” and takes first position)

må is the modal verb must / have to. It commonly expresses necessity (practical or external):

• jeg må håndtere det = I have to deal with it / I need to take care of it
  You could soften it with bør (should) or burde (ought to), but må is the natural choice if it’s required.

å håndtere literally means to handle / manage / deal with. It’s correct, but can sound slightly formal depending on context. Very common alternatives are:

• ordne det = fix/sort it out (very common, natural)
• ta meg av det = take care of it
• fornye passet = renew the passport (more specific)

Because før introduces a subordinate clause. In Norwegian subordinate clauses, the word order is typically subject + verb (no V2 inversion):

• før jeg bestiller billetter (before I book tickets)
  Main clause word order with inversion would be something else (e.g., after an adverb in first position), but not after før.

Indefinite plural billetter is used when you mean tickets in general, not specific already-identified tickets:

• bestiller billetter = book (some) tickets
• bestiller billettene = book the tickets (specific ones already known in context)