1. carefully observant, attentive
be under the watchful eye of someone
The adjective 'watchful' describes someone who is attentive and who is ready to address problems when they occur. It can also describe being in a state of attentiveness and being ready to act if changes are about to take place. This is an adjective you will hear used equally in social and professional contexts. Similar in meaning to 'attentive' and 'observant'.