Cheerfully, Algy strays out of line (5)
I believe the answer is:
gaily
'cheerfully' is the definition.
(thesaurus)
'algy strays out of line' is the wordplay.
'strays' indicates an anagram.
'out of' is an insertion indicator.
'line' becomes 'i' (I can't justify this - if you can you should give a lot more credence to this answer).
'algy' with letters rearranged gives 'galy'.
'galy' going around 'i' is 'GAILY'.
Can you help me to learn more?
(Other definitions for gaily that I've seen before include "Cheerily, brightly" , "In merry or light-hearted manner" , "Merrily" , "Light-heartedly" .)