Eğitim salonu ne kadar dolu olursa olsun kontenjanı artırmayacağız.

A close natural translation is:

No matter how full the training room is, we will not increase the capacity/quota.

Piece by piece:

• Eğitim salonu = training room / training hall
• ne kadar = how much / how ...; here it means however or no matter how
• dolu = full
• olursa olsun = no matter if it is / however it may be
• kontenjanı = the quota / capacity / number of available places
• artırmayacağız = we will not increase

So the overall structure is:

Even if the training room is very full, we will not increase the number of places.

This is a very common Turkish pattern meaning:

• no matter how ...
• however ...
• regardless of how ...

So:

• ne kadar dolu olursa olsun = no matter how full it is

With adjectives, ne kadar often works like however in English:

• ne kadar zor olursa olsun = no matter how difficult it is
• ne kadar pahalı olursa olsun = no matter how expensive it is

Here it does not literally ask a question like how full?
Instead, it creates a concessive meaning: however full the room may be.

Because olursa olsun is a set pattern in Turkish.

Breakdown:

• olursa = if it is / if it becomes
• olsun = let it be / may it be

But together, ... olursa olsun usually functions as one expression meaning:

• no matter ...
• regardless of ...
• whatever the case may be

So you should not translate it too mechanically word by word.
In real usage, the whole chunk ne kadar dolu olursa olsun simply means no matter how full it is.

You will see the same pattern in many phrases:

• Ne olursa olsun = no matter what happens / whatever happens
• Kim olursa olsun = no matter who it is
• Nerede olursa olsun = no matter where it is

Because dolu is an adjective meaning full, while dolmak is a verb meaning to fill up / become full.

So:

• dolu = full
• dolu olmak = to be full
• dolmak = to become full / to get filled

In this sentence, Turkish uses the adjective-based structure:

• dolu olursa = if it is full / if it becomes full

That fits well with ne kadar, which describes degree:

• ne kadar dolu = how full / however full

If you said ne kadar dolarsa, it would sound less natural here, because ne kadar is pairing with the adjective dolu rather than with the verb dolmak.

Here, -u is not the accusative.
It is the ending used in a common Turkish noun-compound pattern.

• eğitim = training / education
• salon = hall / room
• eğitim salonu = training hall / training room

This is like other Turkish compounds:

• spor salonu = sports hall
• toplantı salonu = meeting room
• konferans salonu = conference hall

In this pattern, the second noun often takes a form that looks like a possessive ending:

• salon-u

So eğitim salonu means training room, not the training room because of the -u.
It is just how this kind of compound is formed.

This is important because learners often confuse:

• salonu in eğitim salonu = part of the compound
• kontenjanı in this sentence = accusative direct object

They look similar on the surface, but they are doing different jobs.

Kontenjan usually means:

• quota
• capacity
• number of available places
• enrollment cap

In this sentence, it most likely means the allowed number of participants/places, not just the physical size of the room.

So:

• kontenjanı artırmak = to increase the quota/capacity / to add more spots

Here, kontenjanı has the definite accusative ending -ı, because it is the specific direct object of the verb artırmak.

Compare:

• kontenjan artırmak = to increase capacity in a general sense
• kontenjanı artırmak = to increase the capacity / that capacity

In English we often just say increase capacity or increase the number of places.

It breaks down like this:

• artır- = increase, raise
• -ma- = negation
• -yacak = future tense
• -ız = we

So:

• artırmayacağız = we will not increase

More literally:

• artır-ma-y-acak-ız

The y is just a buffer sound between vowels.

A few similar forms:

• artıracağız = we will increase
• artırmayacağım = I will not increase
• artırmayacaklar = they will not increase

Because Turkish normally places the main verb at the end.

So the structure here is:

• subordinate clause first: Eğitim salonu ne kadar dolu olursa olsun
• main clause after that: kontenjanı artırmayacağız

This is very typical Turkish word order.

A rough structural view:

• No matter how full the training room is
  • we will not increase the quota

In English, the verb often appears earlier, but in Turkish the final verb is the default pattern.

It can suggest both, depending on context, but the most likely meaning is:

• the room/class is very crowded or full
• even so, they will not open more places or accept more participants

Because of kontenjan, the sentence strongly points to capacity in terms of enrollment or allowed participants, not just the room’s physical dimensions.

So in practical English, this could mean:

• Even if the training room is packed, we won’t add more spots.
• No matter how full the class is, we won’t increase the capacity.

Yes. Turkish has a few other ways to express a similar idea. For example:

• Eğitim salonu ne kadar dolu olsa da kontenjanı artırmayacağız.
• Eğitim salonu çok dolu olsa bile kontenjanı artırmayacağız.

These are close in meaning, but ne kadar ... olursa olsun is especially good for no matter how ....

So in your sentence, that pattern is a very natural choice because it emphasizes:

Regardless of the degree of fullness, the decision will not change.