Adopt, keep, etc. a high/low profile - Idioms by The Free Dictionary
adopt, keep, etc. a high/low profile
keep a low profile
To avoid drawing attention, scrutiny, or observation to oneself. A: "I haven't seen you in awhile—how are you?" B: "Oh, I'm fine, just keeping a low profile so I can finish my research by the deadline." It's hard for celebrities to keep a low profile when they go out in public.
adopt, keep, etc. a ˌhigh/ˌlow ˈprofile try/try not to attract other people’s interest, attention, etc: If I were you, I’d try and keep a low profile until she’s forgotten about the whole thing. ♢ In the run-up to the elections all three candidates maintained a high profile.