Dirtiest part of the Solar System (5)
I believe the answer is:
earth
'solar system' is the definition.
(thesaurus)
'dirtiest part of the' is the wordplay.
'dirtiest' becomes 'ar' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'part' is an insertion indicator (the inserted letters split open or part the word).
'of' indicates an anagram (the answer comes from or 'of' the letters).
'the' anagrammed gives 'eth'.
'ar' put into 'eth' is 'EARTH'.
Can you help me to learn more?
(Other definitions for earth that I've seen before include "Ground - globe - soil" , "Third planet from the Sun" , "dirt" , "Terra firma" , "brownish pigment?" .)