Contingent on English failing to deepen cavity (9)
I believe the answer is:
dependent
'contingent on english failing' is the definition.
'dependent' can be an answer for 'contingent' (thesaurus). I'm not sure about the 'on english failing' bit.
'deepen cavity' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'deepen' is 'epende' which is within the answer.
This may be the basis of the clue (or it may be nonsense).
'to' acts as a link.
Can you help me to learn more?
(Other definitions for dependent that I've seen before include "Relying/contingent (on)" , "Reliant" , "Subject" .)