Answer old phone after just oddly leaving car (10)
I believe the answer is:
automobile
'car' is the definition.
(synonyms)
'answer old phone after just oddly' is the wordplay.
'answer' becomes 'a' (abbreviation eg in Q and A).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'phone' becomes 'mobile' (I've seen this before).
'after' means one lot of letters go next to another.
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
The alternate letters of 'just' are 'ut'.
'o'+'mobile'='omobile'
'omobile' put after 'ut' is 'utomobile'.
'a'+'utomobile'='AUTOMOBILE'
'leaving' acts as a link.
(Other definitions for automobile that I've seen before include "American car" , "It may transport" .)