Intensive publicity could get one over-excited, no end (4)
I believe the answer is:
hype
'intensive publicity' is the definition.
(I've seen this before)
'one over-excited no end' is the wordplay.
'one over excited' becomes 'hyper' (I've seen this before).
'no end' means to remove the last letter.
'hyper' with its final letter removed is 'HYPE'.
'could get' acts as a link.
(Other definitions for hype that I've seen before include "racket" , "Puffery" , "Misleadingly exaggerated publicity" , "used by pusher?" , "Plug" .)