Private chat in centre — listen with child outside (5-2-5)
I believe the answer is:
heart-to-heart
'private chat' is the definition.
(private or intimate conversation)
'centre listen with child outside' is the wordplay.
'centre' becomes 'heart' (synonyms).
'listen with' becomes 'hear' (I've seen this before. I am not sure about the 'with' bit.).
'child' becomes 'tot' (term for a young child).
'outside' means one lot of letters goes inside another.
'hear' put into 'tot' is 'toheart'.
'heart'+'toheart'='HEART-TO-HEART'
'in' is the link.
(Other definitions for heart-to-heart that I've seen before include "Intimate conversation" , "Candid conversation" , "Intimate talk" .)