Learn Hardcore Icelandic: Undirskriftin er skýr.

a clear signature: skýr undirskrift (adjective before an <a class="border-b border-dotted border-blue-400 dark:border-blue-500 cursor-pointer text-inherit no-underline" href="/grammar/icelandic/nouns/definite-vs-indefinite">indefinite noun ; strong form)
the clear signature: skýra undirskriftin or hin skýra undirskrift (with a definite noun; weak form skýra )

Undirskrift-in = signature + the; the subject (feminine nominative singular). Built from undir (under) + skrift (writing) with the definite ending -in.
er = is; 3rd person singular of vera (to be); the copula.
skýr = clear; a predicate adjective describing the subject.

Why does the noun end in -in? Where is “the”?

Icelandic uses a suffixed definite article. For feminine nouns in nominative singular, the ending is -in. So undirskrift → undirskriftin = “the signature.” (For reference: masculine -inn, feminine -in, neuter -ið.)

What gender/case/number is undirskriftin, and why?

It’s feminine nominative singular. It’s the subject of the sentence, and subjects of the copula vera (“to be”) are in the nominative. The final -t in undirskrift is part of the root; it doesn’t make the noun neuter.

Why is the adjective skýr and not skýrt or skýra?