I don’t believe “Est un avocat” is a grammatical sentence, although I’m not a native speaker so I can’t say for sure. I’ve never seen a sentence like this.

I would say only “c’est” is possible here.

“Est” and “c’est” are both possible in some circumstances when there is another noun phrase that serves as the subject, but I don’t think they are exactly interchangeable because they can give a different feel to the sentence. I can’t describe the difference perfectly, but in general “est” has a more formal feel, and “c’est” is sometimes informal (although other times “c’est” is idiomatic and acceptable even in formal writing in this kind of context, according to jlliagre’s answer here: La contraction « c'est » peut être après un sujet ?)

For example, “mon frère est un avocat” and “mon frère, c’est un avocat” are both grammatical. (However, Rémi Henry notes in a comment that it would be more common to not use an article: “Mon frère est avocat”. In that case, you would not use c’est: the subject pronoun used before “est avocat” would be il. So subject doubling would result in “Mon frère, il est avocat.”) Note that you are supposed to write a comma before “c’est” in sentences like this.

Similar question: Why is "c'est" used in this sentence and not "est"?

You can’t say “Is a lawyer.” in english. In french it’s the same, you have to answer the question “Who (is a lawyer)?”. In english you would most likely use “he/she” in french we also use the equivalent of “it/this/that” to anwser this question.

Therefore you have three different forms in french:

Il (elle) est avocat(e).

And the one that may look odd to you(?), but is totally fine in french:

C’est un avocat.

It is a composition of “ce” and “est” that has been contracted to “c’est”.

In my opinion you should use one of firsts two if your speech focuses on the person, and the third if the focus is on the job itself. For example if a child asks “who is this guy with the strange dress?” this question obviously concerns the job and you should use “C’est un avocat.” and not “Il est avocat”. Even though the second is correct, it sounds a little strange in this context.

The “c'” of “c’est” is the contraction of “ceci” or “cela” and stands for a virtual subject of the verb. It is a demonstrative one, like “this”, “that”… in English.

You can’t say “Est un avocat.”, as you can’t say “Is a lawyer.” in English.

However you can have in a litterary context something like:

Dans un bureau sombre était un avocat.

It means “there was a lawyer in a dark office” but with a more narrative tone, like if the camera was zooming from the office to the lawyer. After this sentence one would expect a description of this lawyer and this lawyer to be the protagonist of a story.

Anyway, you can’t just remove “c'” and expect the sentence to remain the same.

It’s not a problem of implicit subject of a verb.

Est is, in the meaning of your example, acting as a copula.

It means that it does not carry any meaning. It just links two words together, Generally a subject and an attribute.

Est does not carry any meaning ? If you omit one of the two members then… it is not even a copula!

Hence… what does it stand for ? Nothing! What purpose does it serve ? None!

And therefore serving absolutely no purpose, if you remove the subject, **remove it as well! :

– Qui est ce type qui vient dans sa robe noire ?

– Un avocat!

English are French are same in this case, in contrary of Italian and Spanish.

When you write (or speak) in English, there is always something like Subject + Verb + Complement, in order to be able to identify each elements. So you need a subject if you have a verb in your sentence (there is a few particular case where we don’t use subject, but it’s rarely use).

Take an example : If I say J’aime les oranges

• J' is the pronoun Je contracted because verb next begins with a vowel (means I in English)
• aime is the verb (means like)
• les oranges is the complement, also named COD in French because we know directly what it is, and les is just here for numbers but it’s off-topic to explain it here (means oranges)

So if do a translation in English, we have I like oranges, which have the same structure

About C'est, it’s as simple as our previous example :

• C' is the contraction of ce/ceci/cela (that word differs in function of the sentence/subject), in your case, it means ceci
• est is our verb (être on infinitive form)
• un avocat is our complement, but your word can have 2 meaning :
  • a people (lawyer)
  • a vegetable (avocado)

Yeah, in French, we love to have 2 differents things that are written the same way

So if you don’t like contraction, you can say Ceci est un avocat, but it looks more formal (both in write or speak)