Hanger-on starts to be unreasonably resolute (3)
I believe the answer is:
bur
'hanger-on' is the definition.
(type of seed which hangs onto clothing)
'starts to be unreasonably resolute' is the wordplay.
'starts to' indicates taking the first letters.
The first letters of 'be unreasonably resolute' is 'BUR'.
(Other definitions for bur that I've seen before include "Seed-case" , "small drill" , "sticker" , "Clinging seed case" , "Prickly seed case" .)