Previously having had a success with the other composition (8)
I believe the answer is:
hitherto
'previously' is the definition.
(thesaurus)
'success with the other composition' is the wordplay.
'success' becomes 'hit' (hit is a kind of success).
'with' says to put letters next to each other.
'composition' indicates anagramming the letters.
'other' is an anagram of 'herto'.
'hit'+'herto'='HITHERTO'
'having had a' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for hitherto that I've seen before include "Up to this time" , "Previously" , "Up to this point" , "So far" , "Up till now" .)