Right in the cooking pot there's a pennant (8)
I believe the answer is:
streamer
'there's a pennant' is the definition.
(synonyms)
'right in the cooking pot' is the wordplay.
'right' becomes 'r' (common abbreviation).
'in the' is an insertion indicator.
'cooking pot' becomes 'steamer' (pot for steaming things).
'r' put into 'steamer' is 'STREAMER'.
(Other definitions for streamer that I've seen before include "Heavy cold" , "Banner, flag; fishing fly" , "It blows in the wind" , "bold headline" , "shocking cold?" .)