Advertise seaside attraction, observe, not the first (7)
I believe the answer is:
promote
'advertise' is the definition.
(I know that advertise can be written as promote)
'seaside attraction observe not the first' is the wordplay.
'seaside attraction' becomes 'prom' (promenade).
'observe' becomes 'note' (synonyms).
'not the first' means to remove the first letter.
'note' with its first letter taken off is 'ote'.
'prom'+'ote'='PROMOTE'
(Other definitions for promote that I've seen before include "Publicise; raise in rank" , "Advocate, advance" , "Raise to a more senior position" , "Encourage - upgrade" , "Contribute to progress or growth" .)