Give encouragement: 'Catch -- catch up!' (7)
I believe the answer is:
hearten
'give encouragement catch catch up' is the definition.
I can't judge whether this defines the answer.
'catch catch up' is the wordplay.
'catch' becomes 'hear' (to catch something is to hear it being spoken).
'catch' becomes 'net' (netting is a kind of catching).
'up' is a reversal indicator (in down clue: letters go upwards).
'net' in reverse letter order is 'ten'.
'hear'+'ten'='HEARTEN'
Can you help me to learn more?
(Other definitions for hearten that I've seen before include "Make cheerful" , "Inspirit" , "Comfort" , "Make (someone) more confident" , "Inspire anew" .)