Við endurnýjum samninginn með viðauka og framlengjum leigutímann.

Because they are both 1st person plural present tense forms: we renew and we extend.

• við = we
• endurnýjum = we renew
• framlengjum = we extend

The ending -um is the normal present-tense ending for many verbs with við.

Their infinitives are:

• að endurnýja = to renew
• að framlengja = to extend

So:

• við endurnýjum = we renew
• við framlengjum = we extend

Because they are direct objects of the verbs, so they appear in the accusative case.

• samningur = nominative singular, a contract

• samninginn = accusative singular definite, the contract

• leigutími = nominative singular, a rental period / lease term
• leigutímann = accusative singular definite, the rental period / lease term

In this sentence:

• endurnýjum samninginn = renew the contract
• framlengjum leigutímann = extend the lease term

A very common pattern in Icelandic is that the verb takes a direct object in the accusative.

It marks the definite article, meaning the.

Unlike English, Icelandic usually adds the to the end of the noun instead of putting it before the noun.

So:

• samning = contract

• samninginn = the contract

• leigutíma = lease term
• leigutímann = the lease term

The exact form of the ending changes depending on gender, number, and case, which is why one noun has -inn and the other has -ann.

The preposition með normally takes the dative case when it means with.

So here:

• með = with
• viðauka = dative singular of viðauki = addendum / appendix

So með viðauka means with an addendum.

A useful thing to notice is that for this noun, the accusative and dative singular look the same: viðauka. So even if the form looks familiar, after með it is functioning as a dative.

Because Icelandic often leaves out a repeated subject when two verbs share the same subject.

So:

• Við endurnýjum samninginn ... og framlengjum leigutímann

  means

• We renew the contract ... and extend the lease term

English does the same thing:

• We renew the contract and extend the lease term

You could repeat við, but it is normally unnecessary here.

They are similar in legal or administrative contexts, but they are not the same.

• að endurnýja = to renew
  • make something valid again, replace it with a renewed version, or continue it formally
• að framlengja = to extend
  • make a period of time last longer

In this sentence, that distinction matters:

• endurnýja samninginn = renew the contract
• framlengja leigutímann = extend the lease term

So the contract is renewed, and the actual rental period is extended.

Because Icelandic very often forms compound nouns.

Here:

• leiga = rent / lease
• tími = time / period

Together:

• leigutími = rental period / lease term

Then in the sentence it becomes:

• leigutímann = the lease term in the accusative definite singular

Compound nouns are extremely common in Icelandic, much more so than many English learners first expect.

Yes, that is a very natural nuance here.

Literally, með means with, but in a sentence like this, með viðauka often implies by means of an addendum or through an addendum.

So the phrase can suggest the legal mechanism:

• We renew the contract by means of an addendum and extend the lease term

That is often how this kind of wording works in formal or legal Icelandic.

Yes. It is very normal and straightforward.

The structure is basically:

• Við = subject
• endurnýjum = verb
• samninginn = object
• með viðauka = prepositional phrase
• og framlengjum = coordinated second verb
• leigutímann = second object

So the sentence follows a standard main-clause pattern.

It is also worth knowing that Icelandic is a verb-second language in main clauses. In this sentence, the subject comes first, so the verb naturally comes right after it:

• Við endurnýjum ...

If another element were moved to the front, the verb would still stay in second position.

Because Icelandic and English do not always use definiteness in exactly the same way.

Here, með viðauka is indefinite in form:

• viðauka = an addendum

If Icelandic wanted to say with the addendum, it would normally be:

• með viðaukanum

But in legal or administrative language, Icelandic often uses an indefinite noun where English may choose either an or the, depending on context. So með viðauka is perfectly natural.

The dictionary forms are:

• samningur = contract
• viðauki = addendum / appendix
• leigutími = rental period / lease term

In the sentence, they appear in declined forms:

• samninginn = accusative singular definite of samningur
• viðauka = dative singular of viðauki after með
• leigutímann = accusative singular definite of leigutími

This is a very typical Icelandic learning issue: the form you see in a sentence is often not the dictionary form.