Talk to an eccentric old goat periodically in city (11)
I believe the answer is:
chattanooga
'city' is the definition.
(I have seen 'City of Tennessee' mean 'chattanooga' so perhaps 'city' could also mean 'chattanooga')
'talk to an eccentric old goat periodically' is the wordplay.
'talk' becomes 'chat' (chat can mean to talk).
'eccentric' is an anagram indicator.
'old' becomes 'o' (abbreviation).
'periodically' means one should take alternating letters (letters must be selected 'every so often').
The alternating letters of 'goat' are 'ga'.
'to'+'an'='toan'
'toan' is an anagram of 'tano'.
'chat'+'tano'+'o'+'ga'='CHATTANOOGA'
'in' acts as a link.
(Other definitions for chattanooga that I've seen before include "US town" , "US city" , ""Choo-choo" city in Tennessee" , "17 [TENNESSEE] city" , "US choo-choo destination?" .)