Wife with finger on pulse becomes party disciplinarian (4)
I believe the answer is:
whip
'party disciplinarian' is the definition.
(I've seen this in another clue)
'wife with finger on pulse' is the wordplay.
'wife' becomes 'w'.
'with' means one lot of letters go next to another.
'finger on pulse' becomes 'hip' (I can't justify this - if you can you should give a lot more credence to this answer).
'w'+'hip'='WHIP'
'becomes' acts as a link.
Can you help me to learn more?
(Other definitions for whip that I've seen before include "Strike with strap" , "Political officer who ensures party members attend and vote" , "Address insultingly" , "Strike with lash or rod" , "cat" .)