Notice that lady's poodle at last finding stick (6)
I believe the answer is:
adhere
'stick' is the definition.
(synonyms)
'notice that lady's poodle at last' is the wordplay.
'notice' becomes 'ad' (both can mean an advertisement).
'that lady' becomes 'her' ('her' refers to a woman).
'at last' suggests the final letters.
The last letter of 'poodle' is 'e'.
'ad'+'her'+'e'='ADHERE'
'finding' is the link.
(Other definitions for adhere that I've seen before include "Stick with header" , "Stick to as by suction" , "Header (anag)" , "Stick - join" , "Agree" .)