Prijaviću se jer je ponuda dobra i želim da se zaposlim.

This is the Serbian future tense. The clitic ću is the 1st person singular future auxiliary. When it comes after an infinitive ending in -ti, that ending drops and the result is written as one word:

• prijaviti + ću → prijaviću

So Prijaviću se means I will apply / I’m going to apply.

A very common alternative is:

• Ja ću se prijaviti

That means the same thing.

Yes. Both are correct.

• Prijaviću se = neutral, compact
• Ja ću se prijaviti = also correct, with ja added for emphasis or clarity

Serbian often omits subject pronouns when they are already clear from the verb ending, so ja is not necessary here.

Here prijaviti se means to apply, to sign up, or to register oneself, depending on context.

In this sentence, because ponuda means offer, the most natural interpretation is to apply.

The se matters. Compare:

• prijaviti se = to apply / sign oneself up
• prijaviti nekoga/nešto = to report someone/something, or to register something

So with se, the meaning shifts to something like put myself down as a candidate/applicant.

Because je is a clitic, and Serbian clitics usually go in the second position of their clause.

So the natural order is:

• jer je ponuda dobra

not usually:

• jer ponuda je dobra

The second version sounds marked or unnatural in ordinary speech.

This same second-position rule also helps explain why you get:

• da se zaposlim
• Prijaviću se

with se placed very early in the clause.

Because dobra has to agree with ponuda.

• ponuda is feminine singular
• the adjective must also be feminine singular
• so you get dobra

Compare:

• dobar posao = a good job
• dobra ponuda = a good offer
• dobro mesto = a good place

Here da introduces a subordinate clause after želim.

In English, you would usually say:

• I want to get a job
• I want to become employed

In Serbian, after verbs like want, can, must, plan, and many others, it is very common to use:

• da + present-tense verb

So:

• želim da se zaposlim
  literally works like
• I want that I get employed,
  but in natural English it is simply
• I want to get a job

Because after da, Serbian often uses a present-tense form to talk about something wanted, planned, possible, or expected.

So zaposlim is grammatically a present form, but in this structure it does not mean I am getting employed right now. It means something like:

• that I get employed
• that I become employed
• that I get a job

The future meaning comes from the whole expression želim da... and from context.

Zaposliti se means to get employed, to become employed, or more naturally in English, to get a job.

Again, se is important:

• zaposliti nekoga = to employ someone
• zaposliti se = to get employed oneself

So the sentence contains two different reflexive verbs:

• prijaviti se
• zaposliti se

The two instances of se are not accidental repetition; each one belongs to its own verb.

This is another effect of clitic placement.

Se is a clitic, and clitics tend to come very early in the clause, usually in second position. In:

• da se zaposlim

the word da comes first, so se comes right after it.

That is why you do not normally say:

• da zaposlim se

The standard order is:

• da se zaposlim

It is from the perfective verb zaposliti se.

That matters because perfective aspect focuses on reaching the result:

• zaposliti se = to get employed, to succeed in becoming employed

So in this sentence, the speaker wants the result of becoming employed, not just the ongoing process.

That is why da se zaposlim fits very well here. It sounds like:

• I want to get a job
• I want to become employed

Yes, very possibly. Serbian often leaves out information that is obvious from context.

A fuller version might be:

• Prijaviću se na konkurs = I’ll apply for the competition/opening
• Prijaviću se na oglas = I’ll apply to the ad
• Prijaviću se za posao = I’ll apply for the job

In your sentence, that extra part is omitted because the context already makes it clear what the speaker wants to apply for.

A helpful breakdown is:

• Prijaviću se = I will apply / I’ll sign up
• jer = because
• je = is
• ponuda = offer
• dobra = good
• i = and
• želim = I want
• da = to / that
• se zaposlim = get employed / get a job

So the structure is very close to:

• I’ll apply because the offer is good and I want to get a job.