Fortune-teller's line swallowed by old people (6)
I believe the answer is:
oracle
'fortune-teller's' is the definition.
(I've seen this in another clue)
'line swallowed by old people' is the wordplay.
'line' becomes 'l' (used when specifying particular lines from a poem).
'swallowed by' is an insertion indicator.
'old' becomes 'o' (abbreviation).
'people' becomes 'race' (people can mean a national group or race).
'o'+'race'='orace'
'l' placed into 'orace' is 'ORACLE'.
(Other definitions for oracle that I've seen before include "A famous one at Delphi" , "source of revelation?" , "Soothsayer" , "Source of prophecies" , "Fount of divine inspiration" .)