A recent The Hindu Cryptic crossword of mine (THC #13543) featured this clue:

5d. Saga this distant relative of mine misused for cheap magazines? (10)

This is a "Composite Anagram" (CA, also called a "Compound Anagram") and is considered an "advanced" clue type. I say, piffle to that! I think it's quite straightforward, once you've worked a few out. It's the only clue type where the definition part can be found in the middle of the clue (it can also be at either end, of course).

You can find many explanations on the web, but I think my explanation is better (of course :-)). Just like a normal anagram clue, a CA has two parts, X and Y, and the clue's cryptic reading tells you that X is an anagram of Y (it can do so in a variety of ways, like Angering X gives Y, or X is Y after adjustments, or X rearranges to Y, etc.—the point is that the anagrind can be anywhere as long as the cryptic reading is grammatical).

In a normal anagram clue, one of X/Y is the definition. In a CA, one of X/Y contains the definition as a sub-phrase. It will have other letters (to be included literally in the anagramming) before and/or after the definition part. It is common to indicate a CA with a this [definition], or such a [definition], etc. (but sometimes the setter may not do that and get some raised eyebrows, if the surface without this/such/etc. is just much better).

So, in my clue, X = saga this distant relative of mine, with distant relative of mine being the definition, prefixed by this. The solution is CHIMPANZEE. The anagrind is misused. And, Y = cheap magazines.

(SAGA CHIMPANZEE)* = CHEAP MAGAZINES.

And that's composite anagramming, decomposed.