Bu ceket eski değil; bilakis yeni gibi.

In Turkish, the verb to be is often not stated in simple present-tense sentences.

So:

• Bu ceket eski. = This jacket is old.
• Bu ceket eski değil. = This jacket is not old.

Turkish does not usually need a separate word for is in this kind of sentence. English says is, but Turkish simply puts the adjective after the noun, and that is enough.

Değil is the standard way to negate a noun or adjective predicate in Turkish.

Here:

• eski = old
• değil = not

So:

• eski değil = not old

This is different from negating ordinary verbs, where Turkish often uses verb endings such as -ma / -me.

Compare:

• Bu ceket eski değil. = This jacket is not old.
• Gelmiyor. = He/She is not coming.

So in your sentence, değil is used because eski is an adjective, not a normal action verb.

Because in Turkish, değil normally comes after the word or phrase it negates.

So:

• eski değil = not old
• yorgun değil = not tired
• doktor değil = not a doctor

Putting değil first would sound unnatural or wrong in standard Turkish.

Bilakis means something like:

• on the contrary
• quite the opposite
• rather

So the sentence is not just saying it isn’t old. It goes further and says the opposite idea:

• Bu ceket eski değil; bilakis yeni gibi.
• This jacket isn’t old; on the contrary, it’s like new.

Bilakis is a fairly strong contrast word.

It is understandable and correct, but it sounds a bit formal, literary, or emphatic to many speakers.

In everyday speech, people may more often say things like:

• aksine
• hatta
• or simply leave it out and rely on context

For example:

• Bu ceket eski değil, aksine yeni gibi.
• Bu ceket eski değil, hatta yeni gibi.

So bilakis is good to know, but it is not the most casual everyday choice.

Gibi means like or as if.

So:

• yeni gibi = like new

This does not necessarily mean the jacket is actually new. It means it looks new, or is in very good condition.

Other examples:

• çocuk gibi = like a child
• rüya gibi = like a dream
• eskisi gibi = like before / as it used to be

In your sentence, yeni gibi is a very natural way to say like new.

Usually it means it seems new or it looks as good as new, not that it is literally brand new.

So there is a nuance:

• Bu ceket yeni. = This jacket is new.
• Bu ceket yeni gibi. = This jacket is like new.

That second version often suggests appearance or condition rather than literal newness.

Bu means this, and in Turkish it comes before the noun it modifies.

So:

• bu ceket = this jacket
• bu ev = this house
• bu kitap = this book

That part is actually similar to English word order.

Yes, roughly:

• Bu = this
• ceket = jacket
• eski = old
• değil = not
• bilakis = on the contrary
• yeni gibi = like new

A very literal version would be:

• This jacket old not; on the contrary like new.

That sounds strange in English, of course, but it helps show how Turkish is built.

Not grammatically essential, but it helps show a strong pause and a contrast.

You could also see:

• Bu ceket eski değil, bilakis yeni gibi.

The semicolon just makes the contrast feel a bit clearer or more elegant in writing.

Yes, that is possible, but the emphasis changes.

• Bu ceket eski değil; bilakis yeni gibi.
  This first rejects old, then strengthens it with on the contrary, like new.

• Bu ceket yeni gibi, eski değil.
  This starts with like new, then adds not old. It sounds a little different in focus.

Both are understandable, but the original sentence is more rhetorically polished because of the contrast marker bilakis.

Because here it is simply forming the expression yeni gibi = like new.

In other contexts, gibi can follow nouns, pronouns, or other phrases, sometimes with extra endings before it depending on the structure. But in this sentence, the plain form is enough.

Examples:

• senin gibi = like you
• çocuk gibi = like a child
• yeni gibi = like new

So nothing special is missing; this is the normal form.

Yes, it is grammatical and clear. The only thing to note is style:

• Bu ceket eski değil; bilakis yeni gibi. is correct and slightly formal or emphatic.
• In everyday conversation, many speakers might say:
  • Bu ceket eski değil, aksine yeni gibi.
  • Bu ceket eski değil, yeni gibi.
  • Bu ceket resmen yeni gibi. if they want extra emphasis

So the sentence is natural, but bilakis gives it a somewhat elevated tone.