Learn Italian: Pur essendo stanco, il nonno ci teneva all'artigianato. - Despite being tired, grandfather cared about craftsmanship.

The verb tenerci (to care about something or attach importance to it) requires the preposition a before the object you care about. Since the noun is l'artigianato (craftsmanship), the preposition combines with the definite article to form the articulated preposition all'.

If we explicitly say all'artigianato, why do we still need the ci in ci teneva? Doesn't ci replace the a phrase?

That's a great observation! Normally, ci replaces an a + [topic] phrase so you don't have to repeat it. However, tenerci has become a fixed pronominal verb meaning "to care about." In everyday Italian, the ci is kept as a permanent part of the verb to distinguish its meaning from the regular verb tenere (to hold/keep), even when the object is explicitly stated right after it.

How does pur essendo stanco translate to "despite being tired"? What is pur doing here?

The word pur (a shortened form of pure) combined with a gerund (like essendo, meaning "being") is a very common way to express "even though" or "despite" in Italian. B2 learners love this structure because it means the same thing as sebbene or nonostante but lets you use a simple gerund instead of conjugating a verb in the subjunctive!