Street band, Troy, casually accepting His Eminence's explanation of everything? (6,6)
I believe the answer is:
string theory
'explanation of everything?' is the definition.
(string theory is a theory in physics)
'street band troy casually accepting his eminence's' is the wordplay.
'street' becomes 'st' (abbreviation).
'band' becomes 'ring' (a ring is a band of metal).
'casually' indicates anagramming the letters (I've seen this in other clues).
'accepting' indicates putting letters inside (inserted letters are accepted).
'his eminence' becomes 'he'.
'troy' with letters rearranged gives 'tory'.
'tory' placed around 'he' is 'theory'.
'st'+'ring'+'theory'='STRING THEORY'
(Other definitions for string theory that I've seen before include "One idea in particle physics" , "Idea relating to subatomic particles" , "Cosmological hypothesis concerning all fundamental particles - retrying tosh (anag)" .)