Taking time with request, extremely competitive military group (4,5)
I believe the answer is:
task force
'military group' is the definition.
(military group with a particular mission)
'taking time with request extremely competitive' is the wordplay.
I cannot really understand how this works, but
'time' could be 't' (abbreviation) and 't' is located in the answer.
'request' could be 'askfor' (synonyms) and 'askfor' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for task force that I've seen before include "specially-trained unit" , "Group formed for a specific purpose" , "Temporary unit to accomplish an objective" , "Group for special operation" , "Group assembled for a particular undertaking" .)