Tests new axes around military, primarily (5)
I believe the answer is:
exams
'tests' is the definition.
('exam' can be a synonym of 'test')
'new axes around military primarily' is the wordplay.
'new' indicates an anagram.
'around' indicates putting letters inside.
'primarily' suggests taking the first letters.
The initial letter of 'military' is 'm'.
'axes' is an anagram of 'exas'.
'exas' enclosing 'm' is 'EXAMS'.
(Other definitions for exams that I've seen before include "Knowledge tests" , "Tests, in short" , "Set of exercises evaluating knowledge (abbr)" , "School tests" , "Student assessments" .)