Unusually tiny, listens with determination (11)
I believe the answer is:
insistently
'with determination' is the definition.
(in a determined or insistent way)
'unusually tiny listens' is the wordplay.
'unusually' indicates an anagram.
'tiny'+'listens'='tinylistens'
'tinylistens' anagrammed gives 'INSISTENTLY'.
(Other definitions for insistently that I've seen before include "without let-up" , "in compelling style" .)