Give notice about advanced survey (8)
I believe the answer is:
appraise
'survey' is the definition.
(synonyms)
'give notice about advanced' is the wordplay.
'give notice' becomes 'apprise' (synonyms).
'about' indicates putting letters inside.
'advanced' becomes 'a'.
'apprise' going around 'a' is 'APPRAISE'.
(Other definitions for appraise that I've seen before include "Judge" , "Assess or evaluate" , "Assess value of (something)" , "Estimate or assess the value of" , "Assess, set a price on" .)