McGimpsey was born in Donaghadee, County Down and was educated in Regent House Grammar School and Trinity College, Dublin. He is a businessman aside from politics involved in property development, hotels and the hospitality sector. In the mid-1980s he came to prominence alongside his brother Christopher when they challenged the Anglo-Irish Agreement by bringing a suit against the Irish government in the High Court of the Republic of Ireland, arguing that the Agreement was invalid because it contradicted Articles 2 and 3 of the Constitution of Ireland (this argument was unusual coming from Unionists because of the traditional Unionist opposition to these two articles.) The case failed in the High Court, and again on appeal to the Supreme Court.