Begin introducing a medic at Yankee pre-match bash (4,5)
I believe the answer is:
stag party
'pre-match bash' is the definition.
(party before a wedding)
'begin introducing a medic at yankee' is the wordplay.
'begin' becomes 'start' (synonyms).
'introducing' indicates putting letters inside (some letters introduced or inserted into others).
'a medic at' becomes 'gpa' (I can't justify this - if you can you should believe this answer much more).
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'start' going around 'gpa' is 'stagpart'.
'stagpart'+'y'='STAG-PARTY'
(Other definitions for stag party that I've seen before include "event before wedding" , "All male whoopee night" , "Do for blokes" , "Men only social night out" , "Rollicking night out for men" .)