Bump into them unexpectedly and manage to get leading academic angry (3,6)
I believe the answer is:
run across
'bump into' is the definition.
(thesaurus)
'get leading academic angry' is the wordplay.
'get' becomes 'run' (running is a kind of getting).
'leading' indicates taking the first letters (the leading letter of the word).
'angry' becomes 'cross' (cross can mean annoyed or angry).
The first letter of 'academic' is 'a'.
'run'+'a'+'cross'='RUN ACROSS'
'them unexpectedly and manage to' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for run across that I've seen before include "Quickly reach the other side" , "what this answer doesn't do" , "By chance encounter" , "Chance upon" , "Unexpectedly meet" .)