Perhaps this is a gift that your friend gave to you last year.
这里用定语从句 , 先行词是 gift, that从句来修饰它。 that可以省略,也可以用which, 因为这里是充当从句宾语,分为两个分句的话可以看成 This is a gift, 和your friend gave the gift to you last year 从句。
Maybe/Perhaps this present/gift is the one that your friend gave you last year.
Perhaps this is a gift your friend gave you last year.
Maybe the present you give me is an old one from your friend last year.
To some extents,this is an old gift/present your friend gave you last year.
Perhaps/Maybe this is a gift from your friends last year.
Perhaps this is a gift you give your friends last year.