Efterhånden som jeg træner i træningscenteret hver uge, får jeg bedre kondition.

Efterhånden som is a fixed expression that means something like as, gradually as, or little by little as.

It shows that two things develop at the same time:

• I keep training every week
• my fitness improves

So it is not just a time word. It specifically suggests gradual change over time.

Not in this sentence structure.

• efterhånden by itself is an adverb meaning gradually / eventually / over time
• efterhånden som is a conjunction-like expression used to introduce a clause

So:

• Efterhånden bliver jeg stærkere. = Gradually, I get stronger.
• Efterhånden som jeg træner, bliver jeg stærkere. = As I train, I get stronger.

If you want to follow it with a full clause like jeg træner ..., you normally need som.

This is because of the Danish V2 rule in main clauses.

The sentence begins with the subordinate clause:

Efterhånden som jeg træner i træningscenteret hver uge

After that comes the main clause, and in a Danish main clause the finite verb normally comes in second position. So you get:

• får jeg bedre kondition

not

• jeg får bedre kondition

A simpler comparison:

• Jeg får bedre kondition.
• Når jeg træner hver uge, får jeg bedre kondition.

When something else comes first, the verb comes before the subject in the main clause.

Danish does not have a separate progressive form like English am training.

So the simple present træner can cover:

• I train
• I am training
• sometimes even I’ve been training, depending on context

Here jeg træner ... hver uge clearly means a habitual action: I train every week.

So this is completely normal Danish.

Træningscenteret means the gym / the training center.

It is made up of:

• træning = training
• center = center
• træningscenter = training center / gym
• træningscenteret = the training center / the gym

The ending -et is the definite article for many neuter nouns in Danish. Instead of putting a separate word before the noun, Danish often adds the article to the end.

Compare:

• et center = a center
• centeret = the center

So træningscenteret literally works like the training center.

Here i means in.

It is used because the speaker is physically inside the gym/training center:

• jeg træner i træningscenteret = I train in the gym

For places/buildings, i is often the most straightforward choice when you mean inside.

You may sometimes hear other prepositions with places in Danish, depending on habit and context, but i træningscenteret is perfectly understandable and natural.

Both are possible in Danish, but they are used a little differently.

• hver uge = every week
• om ugen = per week / a week

So:

• Jeg træner hver uge. = I train every week.
• Jeg træner tre gange om ugen. = I train three times a week.

In your sentence, hver uge is natural because it emphasizes regular weekly repetition.

If you said tre gange om ugen, that would give a frequency within each week.

Because kondition is being used as an uncountable/abstract noun here, similar to fitness or stamina.

So får bedre kondition means:

• get better fitness
• improve one’s stamina/cardio fitness

This is the most idiomatic way to say it.

You may sometimes see en bedre kondition, but in this kind of general statement, the version without an article sounds more natural.

Not usually.

In Danish, kondition most often means physical fitness, especially cardio fitness, stamina, or endurance.

So in this sentence it means something like:

• better fitness
• better stamina
• better cardiovascular condition

It is a bit of a false friend for English speakers, because English condition is much broader and often means state or quality of something.

Træningscenter is correct and understandable, but in everyday modern Danish many people would more often say fitnesscenter.

So these both work:

• i træningscenteret
• i fitnesscenteret

Many Danes would probably find fitnesscenteret slightly more common in casual speech.

Also, if you mean more than once a week, you might naturally say something like:

• Efterhånden som jeg træner i fitnesscenteret hver uge, får jeg bedre kondition.
• Efterhånden som jeg træner regelmæssigt, får jeg bedre kondition.

So the original sentence is good Danish, but there are slightly more everyday-sounding alternatives.

They all come from the same basic idea: to train.

• at træne = to train
• jeg træner = I train
• træning = training
• træningscenter = training center
• træningscenteret = the training center

A useful pattern in Danish is:

• verb: træne
• noun from the verb: træning
• compound noun: træningscenter

So once you know one of these words, the others become easier to recognize.

A rough English-friendly guide:

• Efterhånden ≈ EF-ter-hawn-den
• træner ≈ TREH-ner
• træningscenteret ≈ TREH-nings-sen-ter-ed
• kondition ≈ kon-di-shon with the stress near the end

A few important points:

• æ in træner is a very common Danish vowel; it is not exactly an English sound, but eh is a decent start.
• å in efterhånden is like a broad aw sound.
• Danish pronunciation is often softer and more reduced than spelling suggests, so listening to native audio is especially helpful.

For learning purposes, getting the rhythm roughly right matters more at first than making every vowel perfect.

Yes, a little.

In the original sentence, hver uge is placed after i træningscenteret:

• jeg træner i træningscenteret hver uge

That is fine. But Danish often allows some movement of adverbials, especially when the meaning stays clear.

For example:

• jeg træner hver uge i træningscenteret
• jeg træner i træningscenteret hver uge

Both are understandable. The original version sounds natural.

In practice, Danish word order is fairly flexible with time/place phrases, but the verb position rules are much stricter than the placement of expressions like hver uge.