La membreco estas nova.

Membreco is a noun built from:

• membr- = the idea of a member
• -ec- = a suffix meaning quality, state, or condition
• -o = the noun ending

So membreco means membership in the sense of the state or condition of being a member.

Because membro and membreco are different words:

• membro = member (a person)
• membreco = membership (the status of being a member)

So La membro estas nova would mean The member is new, which is a different idea.

Not always. English membership can mean either:

• the state of being a member, or
• the body of members

Esperanto often separates these more clearly:

• membreco = membership as a status
• membraro = the membership as a group of members

So if you mean the members collectively, membraro may be better.

La is the definite article, like the in English.

So la membreco means the membership, not just membership in a general sense.

Esperanto has only one definite article: la. It does not change for gender, number, or case in its basic form.

Estas is the present-tense form of esti, meaning to be.

One helpful feature of Esperanto is that the verb form does not change with the subject:

• mi estas
• vi estas
• li estas
• ĝi estas
• ili estas

So estas works for the membership is just as it would for other subjects.

In Esperanto, adjectives end in -a.

So:

• nova = new
• granda = big
• bona = good

Here, nova is describing membreco, so it appears as an adjective.

Because nova is a predicate adjective after estas.

In Esperanto, the -n ending is usually used for:

• a direct object, or
• motion toward something

But after esti (to be), the following adjective does not take -n.

So:

• La membreco estas nova. = correct
• La membreco estas novan. = incorrect

Because membreco is singular.

Adjectives in Esperanto agree with the nouns they describe in number and case. Since membreco is singular and not accusative, the adjective is also singular and not accusative:

• membreco → singular
• nova → singular

If the noun were plural, the adjective would also be plural:

• novaj membroj = new members

Yes, but it would mean something slightly different grammatically.

• La membreco estas nova. = a full sentence: The membership is new.
• La nova membreco = just a noun phrase: the new membership

So La nova membreco is not a complete sentence by itself unless more is added.

Yes, Esperanto word order is fairly flexible, but the normal order here is the clearest:

• La membreco estas nova.

A different order like Nova estas la membreco is possible, but it sounds more marked or stylistic, as if emphasizing new.

For a learner, the basic order subject + verb + complement is the safest choice.