'Phone home!' offering top part with small alien (7)
I believe the answer is:
handset
'phone' is the definition.
(I know that handset is a type of phone)
'home offering top part with small alien' is the wordplay.
'offering top part' suggests taking the first letters.
'with' becomes 'and'.
'small' becomes 's' (abbreviation - e.g. clothes size).
'alien' becomes 'et' (extra terrestrial).
The initial letter of 'home' is 'h'.
'h'+'and'+'s'+'et'='HANDSET'
(Other definitions for handset that I've seen before include "Phone receiver" , "part of phone" , "Shed tan (anag.)" , "Part of a telephone" , "controller" .)