The language used by 51 in a battered cage (6)
I believe the answer is:
gaelic
'the language' is the definition.
(Gaelic is an example)
'51 in a battered cage' is the wordplay.
'51' becomes 'LI' (Roman numerals).
'in' means one lot of letters goes inside another.
'a battered' indicates anagramming the letters.
'cage' with letters rearranged gives 'gaec'.
'li' going within 'gaec' is 'GAELIC'.
'used by' acts as a link.
(Other definitions for gaelic that I've seen before include "Irish language or Celtic language of Scotland" , "The native language of Ireland" , "tongue" , "Characteristic of the Celts" , "Speech" .)