Language coming from council eager for backing (6)
I believe the answer is:
gaelic
'language' is the definition.
(Gaelic is an example)
'coming from council eager for backing' is the wordplay.
'coming from' says the answer is hidden in the clue.
'for backing' shows that the letters should be reversed in order.
'cileag' can be found hidden inside 'council eager'.
'cileag' reversed gives 'GAELIC'.
(Other definitions for gaelic that I've seen before include "Language of the Celts" , "Characteristic of the Celts" , "Irish language or Celtic language of Scotland" , "Speech" , "The native language of Ireland" .)