Concerned with giddy period, come back (6)
I believe the answer is:
return
'come back' is the definition.
(synonyms)
'concerned with giddy period' is the wordplay.
'concerned with' becomes 're' (re can mean regarding, concerning).
'giddy period' becomes 'turn' (as in a funny turn).
're'+'turn'='RETURN'
(Other definitions for return that I've seen before include "Comeback" , "Come back with a formal report on transactions" , "'Come, go or bring back (6)'" , "Come back with financial statement" , "Send, bring or come back" .)