Go by Dad’s primary school (4)
I believe the answer is:
pass
'go by' is the definition.
(synonyms)
'dad's primary school' is the wordplay.
'dad's' becomes 'pa's' (pa can mean someone's father).
'primary' suggests taking the first letters.
The initial letter of 'school' is 's'.
'pas'+'s'='PASS'
(Other definitions for pass that I've seen before include "what the Galibier is" , "Go beyond; fail to answer" , "Exceed; leave behind" , "Exceed; mountain route" , "Hand over < identity card" .)