She inspired merry action, periodically (5)
I believe the answer is:
erato
'she inspired' is the definition.
(one of the inspiring muses of mythology)
'merry action periodically' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'merry'+'action'='merryaction'
The alternate letters of 'merryaction' are 'ERATO'.
(Other definitions for erato that I've seen before include "Muse of lyric poetry and mime" , "Poet's muse" , "inspiration for poetry" , "goddess" , "daughter of Zeus" .)