Poke fun at a politician in flier (7)
I believe the answer is:
lampoon
'poke fun at' is the definition.
(lampooning is a kind of poking fun at)
'a politician in flier' is the wordplay.
'politician' becomes 'mp'.
'in' indicates putting letters inside.
'flier' becomes 'loon' (loon is a kind of birdanimal**).
'a'+'mp'='amp'
'amp' going into 'loon' is 'LAMPOON'.
(Other definitions for lampoon that I've seen before include "Piece of writing that ridicules someone" , "send-up" , "Satirical personal attack" , "Satirical work" , "Make fun of" .)