With good intentions, PM’s lacking style going round poor (4-7)
I believe the answer is:
well-meaning
'with good intentions' is the definition.
'going round poor' is the wordplay.
'going' becomes 'welling' (I am not sure about this - if you are sure you should believe this answer much more).
'round' is an insertion indicator.
'poor' becomes 'mean' (similar in meaning).
'welling' placed around 'mean' is 'WELL-MEANING'.
'pm's lacking style' acts as a link.
This may not be correct. Some or all of it may be part of another bit of the clue.
(Another definition for well-meaning that I've seen is " Having good, if sometimes ill-advised, intentions".)