Propositions those desperate to introduce rock band (8)
I believe the answer is:
theorems
'propositions' is the definition.
(I know this)
'those desperate to introduce rock band' is the wordplay.
'desperate' indicates anagramming the letters (a desperate or pathetic spelling).
'to introduce' is an insertion indicator (to introduce to can mean to insert or include).
'rock band' becomes 'rem' (REM are a US rock band).
'those' is an anagram of 'theos'.
'theos' enclosing 'rem' is 'THEOREMS'.
(Other definitions for theorems that I've seen before include "Mathematical propositions" , "Rules" , "Propositions proved by chain of reasoning" , "Propositions proved by chains of reasoning" , "Demonstrable principles" .)