Like non-standard, occasionally-used, musical expression of praise (8)
I believe the answer is:
alleluia
'expression of praise' is the definition.
The definition suggests a singular noun which matches the answer.
'like non-standard occasionally-used musical' is the wordplay.
'like non standard' becomes 'allel' (I am not sure about this - if you are sure you should believe this answer much more).
'occasionally used' indicates alternate letters.
The alternating letters of 'musical' are 'uia'.
'allel'+'uia'='ALLELUIA'
Can you help me to learn more?
(Other definitions for alleluia that I've seen before include "Shout or song in praise of God" , "Liturgical shout of praise" , "Hebrew word meaning praise to God" , "Religious word to express praise or thanks" , "Biblical exhortation of praise to the Lord" .)