Function a new group initiated in shelter (7)
I believe the answer is:
tangent
'function' is the definition.
(tangent is a kind of function)
'a new group initiated in shelter' is the wordplay.
'initiated' suggests taking the first letters.
'in' indicates putting letters inside.
'shelter' becomes 'tent' (canvas shelter).
The initial letters of 'new group' is 'ng'.
'a'+'ng'='ang'
'ang' placed into 'tent' is 'TANGENT'.
(Other definitions for tangent that I've seen before include "line in mathematics" , "Line touching curve at one point" , "Line that touches curve without crossing it" , "Particular line" , "seen to be touching" .)