Complex sentence: He subsequently became organist of St. John's Chapel, Bedford Row, in 1760; and, in succession to his brother, he held the post of "composer" to Vauxhall Gardens from 1753 to 1761, and again from 1770 to 1774.
Split into simpler sentences: He subsequently became organist of St. John's Chapel, Bedford Row, in 1760. He succeeded his brother to hold the post of "composer" to Vauxhall Gardens from 1753 to 1761, and again from 1770 to 1774.