The best part was getting the big score (4,5)
I believe the answer is:
high point
'the best part' is the definition.
(I've seen this before)
'big score' is the wordplay.
'big' becomes 'high' ('high' can be a synonym of 'big').
'score' becomes 'point' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'high'+'point'='HIGH POINT'
'was getting the' acts as a link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for high point that I've seen before include "the best part?" , "The best bit" , "memorable occasion" , "Most successful time" .)