Popular enthusiast playing piece that's childish (9)
I believe the answer is:
infantile
'childish' is the definition.
(synonyms)
'popular enthusiast playing piece' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'enthusiast' becomes 'fan' (fan is a kind of enthusiast).
'playing piece' becomes 'tile' (eg a Scrabble tile).
'in'+'fan'+'tile'='INFANTILE'
'that's' is the link.
(Other definitions for infantile that I've seen before include "Inflate in childish way" , "for kids" , "in early stage of development" , "Babyish" .)