According to The Peerage of Ireland by Edward Kimble (1768), Andrew had 2 sons, Sir George and John, who died unmarried. Sir George died in 1519 and was succeeded by his son, John.
The prefix to The Peerage states that the information has been collected from Parliament Rolls, Family Documents and Personal Information from many Noble Peers. Given the dates and this record, it is more probable that John is Andrew's grandson, not his son.