He rapped about getting to grips with new bust (9)
I believe the answer is:
apprehend
'bust' is the definition.
(I've seen this before)
'he rapped about getting to grips with new' is the wordplay.
'about' indicates an anagram.
'getting to grips with' means one lot of letters goes inside another.
'new' becomes 'n'.
'he'+'rapped'='herapped'
'herapped' anagrammed gives 'apprehed'.
'apprehed' placed around 'n' is 'APPREHEND'.
(Other definitions for apprehend that I've seen before include "Recognise - arrest - suspect" , "Dread; capture" , "Arrest - grasp" , "Detain" , "Catch; understand" .)