watchful
adjective
[ ˈwɒtʃfʊl ]
• watching someone or something closely; alert and vigilant.
• "they attended dances under the watchful eye of their father"
Similar:
observant,
alert,
vigilant,
attentive,
perceptive,
awake,
wakeful,
aware,
heedful,
sharp,
sharp-eyed,
keen-eyed,
eagle-eyed,
hawk-eyed,
gimlet-eyed,
with one's eyes open,
on the lookout,
on the qui vive,
wary,
cautious,
careful,
suspicious,
circumspect,
chary,
with one's eyes skinned/peeled,