Si trenques el got, n'hem de comprar un altre.

Because si without an accent means if.

Catalan also has sí with an accent, but that means yes. In this sentence, the word introduces a condition, so it has to be si.

Trenques is the 2nd person singular present indicative of trencar:

• (tu) trenques = you break

The spelling changes from c to qu before e so the verb keeps the hard k sound.

In Catalan, normal real conditions use si + present indicative:

• Si trenques el got...

This works like English If you break the glass... English also uses the present after if, not will.

So trenques is exactly the form you would expect here.

Haver de + infinitive means to have to / must.

So:

• hem de comprar = we have to buy
• hem = we have

Here haver is not showing possession. It is part of a structure expressing obligation.

Because the speaker is describing a shared consequence:

• If you break the glass, we have to buy another one.

That may mean the cost or responsibility is shared by the speaker and someone else. The subject of the first verb and the subject of the second verb do not have to be the same.

If the meaning were you have to buy another one, Catalan would be:

• Si trenques el got, n'has de comprar un altre.

N' is the shortened form of the weak pronoun en.

Here it refers back to got and tells you that the noun is understood but not repeated. English usually uses one in this situation:

• another one

Catalan often uses en to point back to the omitted noun:

• n'hem de comprar un altre = we have to buy another one

So n' is helping avoid repeating got.

The full pronoun is en, but before a vowel it usually drops its e:

• en + hem → n'hem

The apostrophe just shows that something has been omitted.

Yes, with a verb group like haver de + infinitive, Catalan often allows the weak pronoun in two places:

• n'hem de comprar un altre
• hem de comprar-ne un altre

The version in your sentence puts the pronoun before the conjugated verb hem, which is very common.

Because when altre means another and the noun is omitted, Catalan normally keeps the article:

• un altre = another one

You would also keep it if the noun were stated:

• un altre got = another glass

So altre on its own would not be the normal choice here.

Because it refers back to got, and got is a masculine singular noun:

• el got
• un altre

If the noun were feminine, you would use una altra.

Because they do different jobs.

• el got = a specific glass already understood in the situation
• un altre = another one, a replacement

So first the sentence talks about the glass that might get broken, and then it talks about buying another glass afterward.