If Jan is not careful her gossip will alienate all of her friends. Option C is correct.
The only suitable option to complete the gap after will is a verb. From the options provided the only verb is the word "alienate."
To alienate means making (someone) feel isolated or estranged; causing someone or a group of people to stop supporting and agreeing with you.
Alienate is a transitive verb which may be also defined as to make unfriendly, hostile, or indifferent especially where attachment formerly existed.