Mike pursues a girl with vigour! (3)
I believe the answer is:
vim
'vigour' is the definition.
(I know that vigour can be written as vim)
'mike pursues a girl' is the wordplay.
'mike' becomes 'M' (phonetic alphabet: alpha, bravo, charlie etc.).
'pursues' is a charade indicator (letters next to each other).
'a girl' becomes 'vi' (short for Violet).
'm' after 'vi' is 'VIM'.
'with' acts as a link.
(Other definitions for vim that I've seen before include "Exuberant vigour" , "Pizazz" , "Energy, enthusiasm" , "Pep and energy" , "Liveliness" .)