Penultimate part of Shakespearean play is beginning to move into vigorous campaigning (8)
I believe the answer is:
activism
'vigorous campaigning' is the definition.
'penultimate part of shakespearean play is beginning to move' is the wordplay.
'penultimate part of shakespearean play' becomes 'activ' (fourth of five acts in a Shakespeare play).
'beginning to' suggests taking the first letters.
The first letter of 'move' is 'm'.
'activ'+'is'+'m'='ACTIVISM'
'into' is the link.
(Other definitions for activism that I've seen before include "Policy of vigorous work as in politics" , "Political efforts" .)