The sentence is grammatically correct but it is illogical. "Another" here, means "one more; a further". Normally, a person mentions or refers to one thing/person first before he mentions or refers to another one. It is illogical just like a person walking into a store and says..e.g. "Give me another icecream." when he hasn't even bought one previously!Another friend works in a college.
a) A friend of mine works in a bank. Another friend works in a college.
b) That icecream was great. Give me another one please.