Teams crossing middle of district in steps (7)
I believe the answer is:
strides
'steps' is the definition.
('stride' can be a synonym of 'step')
'teams crossing middle of district' is the wordplay.
'teams' becomes 'sides' (eg football sides).
'crossing' indicates putting letters inside.
'middle of' says to take the centre.
The central letters of 'district' are 'tr'.
'sides' going around 'tr' is 'STRIDES'.
'in' is the link.
(Other definitions for strides that I've seen before include "Trousers; long steps" , "Walks with long steps" , "Daks" , "Long walking steps" , "Trousers (Australian)" .)