Frivolous old man after power in N Wales town (8)
I believe the answer is:
flippant
'frivolous' is the definition.
(similar in meaning)
'old man after power in n wales town' is the wordplay.
'old man' becomes 'pa' (both can mean someone's father).
'after' says to put letters next to each other.
'power' becomes 'p' (symbol in physics).
'in' means one lot of letters goes inside another.
'n wales town' becomes 'Flint' (Flint is a town in North Wales).
'pa' put after 'p' is 'ppa'.
'ppa' inserted into 'flint' is 'FLIPPANT'.
(Other definitions for flippant that I've seen before include "showing disrespectful attitude" , "Not serious or respectful" , "Being facetious over pint flap" , "light" , "anything but serious" .)