Avoided attention (4,1,3,7)
I believe the answer is:
kept a low profile
'avoided attention' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for kept a low profile that I've seen before include "stayed out of the public eye?" , "avoided attracting attention" , "Held on to a Colonel Blimp drawing that's" .)