Poet dismissing popular play (4)
I believe the answer is:
lark
'play' is the definition.
(larking is a kind of playing)
'poet dismissing popular' is the wordplay.
'poet' becomes 'larkin' (Philip Larkin).
'dismissing' suggests deleting specific letters.
'popular' becomes 'in' (something that's 'in' is fashionable).
'larkin' with 'in' taken away is 'LARK'.
(Other definitions for lark that I've seen before include "Foolish activity, songbird" , "Soaring bird" , "Bit of fun - early-rising bird?" , "Rise with this bird to get up early" , "flier" .)