Ask for another search? (7)
I believe the answer is:
request
'ask for' is the definition.
(synonyms)
'another search?' is the wordplay.
'another' becomes 're' (I've seen this in other clues).
'search?' becomes 'quest' (quest is a kind of search).
're'+'quest'='REQUEST'
(Other definitions for request that I've seen before include "Plea" , "Appeal" , "Application" , "Polite demand" , "Suit" .)