A split resolution (12)

I believe the answer is:

perseverance

'resolution' is the definition.
(I know that perseverance is a type of determination)

'a split' is the wordplay.
'a' becomes 'per' (eg 'one a day' means 'one per day').
'split' becomes 'severance' (I've seen this before).
'per'+'severance'='PERSEVERANCE'

(Other definitions for perseverance that I've seen before include "Tenacity, doggedness" , "Continuing endeavour" , "Steady persistence" , "Persistence, indefatigability" , "Determination" .)

I've seen this clue in The Times.

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