Determined a number climbing in fell (9)
I believe the answer is:
diagnosed
'determined' is the definition.
(I've seen this before)
'a number climbing in fell' is the wordplay.
'number' becomes 'song' (I've seen this before**).
'climbing' is a reversal indicator (in a down clue, letters climb up).
'in' means one lot of letters goes inside another.
'fell' becomes 'died'.
'song' backwards is 'gnos'.
'a'+'gnos'='agnos'
'agnos' placed within 'died' is 'DIAGNOSED'.
(Other definitions for diagnosed that I've seen before include "Identified disease" , "Determined" .)