Home near Exeter seems tiny, initially (4)
I believe the answer is:
nest
'home' is the definition.
(a bird's home)
'near exeter seems tiny initially' is the wordplay.
'initially' suggests taking the first letters.
The initial letters of 'near exeter seems tiny' is 'NEST'.
(Other definitions for nest that I've seen before include "Structure built by birds" , "Robin's home" , "A set (of tables)" , "10 [HOUSE]" , "Home to a bird" .)