expression, suru verb (special)
exercise great care; be extremely careful
A formal set phrase meaning to act with the utmost caution, often used in official or serious contexts. The construction is 慎重を期する, where 期する means 'to expect' or 'to ensure', so the phrase literally means 'to ensure prudence'.
See also: 期する
個人情報の取り扱いには慎重を期する必要がある。
We must exercise great care in handling personal information.
The government is being extremely careful with its foreign policy.