El supervisor exige seguimiento.

In Spanish, singular countable nouns usually need an article or another determiner when they are the subject of a sentence.

So Spanish normally says:

• El supervisor exige seguimiento.

Not:

• Supervisor exige seguimiento. ❌

Here, el means the. It tells us we are talking about a specific supervisor, or at least treating supervisor as a normal subject noun phrase.

Exige is the third-person singular present tense form of exigir.

The subject is el supervisor, which is he / she / it grammatically, so the verb must match:

• yo exijo = I demand / require
• tú exiges = you demand / require
• él / ella / usted exige = he / she / you demand / requires

So:

• El supervisor exige... = The supervisor demands / requires...

Seguimiento is a noun, not a verb.

It comes from the idea of seguir (to follow) and often means things like:

• follow-up
• monitoring
• tracking
• oversight, depending on context

So in this sentence, seguimiento is the thing being required or demanded.

Spanish often leaves out the article with an abstract or general noun, especially when talking about something in a broad, non-specific way.

So:

• exige seguimiento = requires follow-up / requires monitoring in general

If you wanted to make it more specific, you could say:

• exige un seguimiento = requires a follow-up / some follow-up
• exige el seguimiento del caso = requires the follow-up of the case

The version without an article sounds general and concise.

Yes. That is possible, but it changes the feel slightly.

• exige seguimiento = requires follow-up in a general sense
• exige un seguimiento = requires a follow-up / requires some kind of follow-up

The sentence without un can sound more institutional, formal, or headline-like. The version with un can sound a little more concrete.

Yes, very common, especially in professional, administrative, medical, and business contexts.

You will often hear things like:

• dar seguimiento = to follow up
• hacer seguimiento = to monitor / follow up
• seguimiento del caso = case follow-up
• seguimiento del proyecto = project monitoring

In Latin America, dar seguimiento is especially common.

Not always exactly.

Exigir often has a stronger tone than English require. It can mean:

• to demand
• to require
• to insist on

So El supervisor exige seguimiento may sound fairly strong, as if the supervisor is insisting that follow-up be done.

Depending on context, English might translate it as either:

• The supervisor requires follow-up
• The supervisor demands follow-up

The masculine form supervisor can sometimes be used generically, but if you are clearly referring to a woman, supervisora is very common and natural.

So you could say:

• La supervisora exige seguimiento.

That would mean The female supervisor requires follow-up.

Because exigir normally takes a direct object with no preposition.

So the structure is:

• alguien exige algo = someone demands/requires something

Examples:

• El supervisor exige resultados.
• La empresa exige puntualidad.
• El supervisor exige seguimiento.

No preposition is needed before seguimiento.

Yes, but El supervisor exige seguimiento is the most neutral and standard order:

• subject + verb + object

Other orders are possible, but they sound more marked or emphatic. For example:

• Seguimiento exige el supervisor.
  This is grammatically possible in some contexts, but it sounds unusual and emphatic.

For normal everyday Spanish, the original order is the best choice.

A simple approximate pronunciation is:

el soo-pehr-bee-SOR ehk-HEE-heh seh-gee-mee-EN-toh

A few notes:

• v and b sound very similar in Spanish
• g in exige sounds like a strong h in most Latin American accents because it comes before e
• gui in seguimiento keeps the hard g sound, so it sounds like gee

A more syllable-by-syllable breakdown:

• El → el
• supervisor → su-per-vi-SOR
• exige → ek-SI-he / ek-HEE-he, depending on accent and pace
• seguimiento → se-gi-mien-to

It is understandable and natural, but it does sound somewhat formal, concise, and professional.

You might see or hear it in contexts like:

• management
• compliance
• medicine
• customer service
• project tracking

In more everyday speech, people might say something slightly longer, such as:

• El supervisor exige que se le dé seguimiento.
• El supervisor pide seguimiento.
• El supervisor quiere seguimiento del caso.

But the original sentence is perfectly valid, especially in formal or written contexts.