vigilant

adjective
vig*i*lant \ ˈvi-jə-lənt \
15th century
  • alertly watchful especially to avoid danger

hypervigilant

adjective
hy*per*vig*i*lant \ ˌhī-pər-ˈvi-jə-lənt \
1905
  • extremely or excessively vigilant : highly or abnormally alert to potential danger or threat

under the eye of

idiom
under the eye of \
  • while being watched by (someone)
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