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.
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 for. And, Y = cheap magazines.
(SAGA CHIMPANZEE)* = CHEAP MAGAZINES.
And that's composite anagramming, decomposed.