Depend on keeping a brave heart in a race (5)
I believe the answer is:
relay
'race' is the definition.
(relay race)
'depend on keeping a brave heart' is the wordplay.
'depend on' becomes 'rely' (to rely on something is to depend on it).
'keeping' indicates putting letters inside (some letters kept inside).
'heart' says to take the centre.
The middle letter of 'brave' is 'a'.
'rely' going around 'a' is 'RELAY'.
'in a' acts as a link.
(Other definitions for relay that I've seen before include "track event" , "Team of workers" , "Pass on - put down again" , "Receive and pass on - race" , "Hand, pass on" .)