Perhaps roofer's chicken after heading to tower (8)
I believe the answer is:
thatcher
'perhaps roofer's' is the definition.
(someone thatching a roof)
'chicken after heading to tower' is the wordplay.
'chicken' becomes 'hatcher' (chickens hatch from eggs).
'after' says to put letters next to each other.
'heading to' suggests taking the first letters (the head of the word).
The first letter of 'tower' is 't'.
'hatcher' after 't' is 'THATCHER'.
(Other definitions for thatcher that I've seen before include "Traditional roof maker" , "Roof-working prime minister" , "Former leader" , "Iron 17 across" , "Roof coverer" .)