Goddess regularly suppressing her reaction (5)
I believe the answer is:
erato
'goddess' is the definition.
(I've seen this before)
'regularly suppressing her reaction' is the wordplay.
'regularly suppressing' means one should take alternating letters (letters removed at regular intervals).
'her'+'reaction'='herreaction'
The alternating letters of 'herreaction' are 'ERATO'.
(Other definitions for erato that I've seen before include "One inspiring" , "daughter of Zeus" , "Muse of lyric poetry and mime" , "Poet's muse" , "Source of poetic inspiration" .)