Every boy and girl got the present;____ was given on New Year's Eve.

I think the semicolon is key here. The word preceding it is the noun 'present'. The word following the semicolon should be a pronoun that is used to mean 'present'. Therefore, it can't be he/she/they - it can only be 'it'.
BTW, A semicolon in the middle of a sentence can't split that sentence into two sentences.
Hope the above helps!