Dive, having breather in physical education (6)
I believe the answer is:
plunge
'dive' is the definition.
('plunge' can be a synonym of 'dive')
'breather in physical education' is the wordplay.
'breather' becomes 'lung' (I've seen this before).
'in' means one lot of letters goes inside another.
'physical education' becomes 'pe'.
'lung' going into 'pe' is 'PLUNGE'.
'having' acts as a link.
(Other definitions for plunge that I've seen before include "Nose-dive" , "Fall suddenly and uncontrollably" , "Dive - submerge" , "Dive or fall headlong" , "Thrust into liquid" .)