に大きな影響を与える

have a great influence on

→ に
phrase Rare #45,530
have a great influence on The particle に marks the person or thing affected. The verb 与える is often conjugated to fit the sentence.
JA: この政策は地域社会に大きな影響を与える可能性がある。
EN: This policy could have a great influence on the local community.