Gossip giving chase round shopping centre (5,4)
I believe the answer is:
small talk
'gossip' is the definition.
(synonyms)
'chase round shopping centre' is the wordplay.
'chase' becomes 'stalk' (stalk is a kind of chase).
'round' means one lot of letters goes inside another.
'shopping centre' becomes 'mall' (a mall is a large shopping complex).
'stalk' going around 'mall' is 'SMALL-TALK'.
'giving' is the link.
(Other definitions for small talk that I've seen before include "Social chat on unimportant matters" , "Polite conversation on trivial matters" , "Social conversation on unimportant matters" , "casual conversation" , "Polite chit-chat" .)