Language used by lousy leader ain't working (5)
I believe the answer is:
latin
'language' is the definition.
(Latin is an example)
'lousy leader ain't working' is the wordplay.
'leader' says to take the initial letters.
'working' indicates anagramming the letters.
The first letter of 'lousy' is 'l'.
'aint' is an anagram of 'atin'.
'l'+'atin'='LATIN'
'used by' acts as a link.
(Other definitions for latin that I've seen before include "and 15 Down: Student area of Paris" , "Language of old Romans" , "Cicero's tongue" , "Language of ancient Rome" , "Learning it 'an honour' (Churchill)" .)