Fine to follow story willingly (though less so these days) (4)
I believe the answer is:
lief
'willingly though less so these days' is the definition.
The definition suggests an adverb but the answer is an adverb.
'fine to follow story' is the wordplay.
'fine' becomes 'f' (abbreviation).
'to follow' is a charade indicator (letters next to each other) (some letters go after or follow others).
'story' becomes 'lie' (story can mean a fabrication).
'f' put after 'lie' is 'LIEF'.
Can you help me to learn more?
(Another definition for lief that I've seen is " In old usage, gladly or willingly - file away".)